def __init__(self, group=0):
self._group = group
self._table = dict()
db = connect_db()
dims = db['dimensions']
emf_logger.debug('dims table ={0}'.format(dims))
emf_logger.debug('group={0}'.format(group))
try: #this checks if there is any information about the group in question, sets rec to {'group': group} when it finds it
if group == 0:
rec = dims.find_one({'group': 'gamma0'})
self.dimension = self.dimension_gamma0
emf_logger.debug('rec={0}'.format(rec['_id']))
elif group == 1:
rec = dims.find_one({'group': 'gamma1'})
self.dimension = self.dimension_gamma1
except: #if rec hasn't been set, then it didn't find the group
rec = None
emf_logger.critical('Critical error: No dimension information for group={0}'.format(group))
if rec!=None:
self._table = loads(rec['data'])
if rec != None:
self._table = loads(rec['data']) #loads the data for the group in _table
else:
self._table = None
if self._table != None:
emf_logger.debug('Have information for levels {0}'.format(self._table.keys()))
def __init__(self, group=0):
self._group = group
self._table = dict()
db = connect_db()
dims = db['dimensions']
emf_logger.debug('dims table ={0}'.format(dims))
emf_logger.debug('group={0}'.format(group))
try: #this checks if there is any information about the group in question, sets rec to {'group': group} when it finds it
if group == 0:
rec = dims.find_one({'group': 'gamma0'})
self.dimension = self.dimension_gamma0
emf_logger.debug('rec={0}'.format(rec['_id']))
elif group == 1:
rec = dims.find_one({'group': 'gamma1'})
self.dimension = self.dimension_gamma1
except: #if rec hasn't been set, then it didn't find the group
rec = None
emf_logger.critical(
'Critical error: No dimension information for group={0}'.
format(group))
if rec != None:
self._table = loads(rec['data'])
if rec != None:
self._table = loads(
rec['data']) #loads the data for the group in _table
else:
self._table = None
if self._table != None:
emf_logger.debug('Have information for levels {0}'.format(
self._table.keys()))
def get_downloads(level=None, weight=None, character=None, label=None, **kwds):
keys = [
'download', 'download_file', 'tempfile', 'format', 'number', 'bitprec'
]
info = get_args(request, level, weight, character, label, keys=keys)
# info = to_dict(request.form)
# info['level']=level; info['weight']=weight; info['character']=character; info['label']=label
if 'download' not in info:
emf_logger.critical(
"Download called without specifying what to download!")
return ""
emf_logger.debug("in get_downloads: info={0}".format(info))
if info['download'] == 'file':
# there are only a certain number of fixed files that we want people to download
filename = info['download_file']
if filename == "web_modforms.py":
dirname = emf.app.root_static_folder
try:
emf_logger.debug("Dirname:{0}, Filename:{1}".format(
dirname, filename))
return send_from_directory(dirname,
filename,
as_attachment=True,
attachment_filename=filename)
except IOError:
info['error'] = "Could not find file! "
if info['download'] == 'coefficients':
info['tempfile'] = "/tmp/tmp_web_mod_form.txt"
return get_coefficients(info)
if info['download'] == 'object':
return download_web_modform(info)
info['error'] = "Could not find file! "
def __init__(self, modulus=1, number=1, update_from_db=True, compute=False):
r"""
Init self.
"""
emf_logger.critical("In WebChar {0}".format((modulus, number, update_from_db, compute)))
if not gcd(number, modulus) == 1:
raise ValueError, "Character number {0} of modulus {1} does not exist!".format(number, modulus)
if number > modulus:
number = number % modulus
self._properties = WebProperties(
WebInt("conductor"),
WebInt("modulus", value=modulus),
WebInt("number", value=number),
WebInt("modulus_euler_phi"),
WebInt("order"),
WebStr("latex_name"),
WebStr("label", value="{0}.{1}".format(modulus, number)),
WebNoStoreObject("sage_character", type(trivial_character(1))),
WebDict("_values_algebraic"),
WebDict("_values_float"),
WebDict("_embeddings"),
WebFloat("version", value=float(emf_version)),
)
emf_logger.debug("Set properties in WebChar!")
super(WebChar, self).__init__(update_from_db=update_from_db)
if self._has_updated_from_db is False:
self.init_dynamic_properties() # this was not done if we exited early
compute = True
if compute:
self.compute(save=True)
# emf_logger.debug('In WebChar, self.__dict__ = {0}'.format(self.__dict__))
emf_logger.debug("In WebChar, self.number = {0}".format(self.number))
def save_to_db(self, update = True):
r"""
Saves ```self``` to the database, i.e.
save the meta record and the file in the gridfs file system.
"""
import pymongo
from pymongo.errors import OperationFailure
fs = self._files
try:
self.authorize()
except OperationFailure:
emf_logger.critical("Authentication failed. You are not authorized to save data to the database!")
return False
file_key = self.file_key_dict()
coll = self._file_collection
if fs.exists(file_key):
emf_logger.debug("File exists with key={0}".format(file_key))
if not update:
return True
else:
fid = coll.find_one(file_key, projection=['_id'])['_id']
fs.delete(fid)
emf_logger.debug("Deleted file with fid={0}".format(fid))
# insert
s = dumps(self.fs_dict())
if not self._use_separate_db:
file_key.update(self.db_dict())
try:
t = fs.put(s, **file_key)
emf_logger.debug("Inserted file t={0}, filekey={1}".format(t,file_key))
except Exception, e:
emf_logger.debug("Could not insert file s={0}, filekey={1}".format(s,file_key))
emf_logger.warn("Error inserting record: {0}".format(e))
def __init__(self, group=0):
self._group = group
self._table = dict()
db = connect_db()
dims = db['dimensions']
emf_logger.debug('dims table ={0}'.format(dims))
emf_logger.debug('group={0}'.format(group))
try:
if group == 0:
rec = dims.find_one({'group': 'gamma0'})
self.dimension = self.dimension_gamma0
emf_logger.debug('rec={0}'.format(rec['_id']))
elif group == 1:
rec = dims.find_one({'group': 'gamma1'})
self.dimension = self.dimension_gamma1
except:
rec = None
emf_logger.critical(
'Critical error: No dimension information for group={0}'.
format(group))
if rec <> None:
self._table = loads(rec['data'])
else:
self._table = None
if self._table <> None:
emf_logger.debug('Have information for levels {0}'.format(
self._table.keys()))
def get_downloads(level=None, weight=None, character=None, label=None, **kwds):
keys = ['download', 'download_file', 'tempfile', 'format', 'number','bitprec']
info = get_args(request, level, weight, character, label, keys=keys)
# info = to_dict(request.form)
# info['level']=level; info['weight']=weight; info['character']=character; info['label']=label
if 'download' not in info:
emf_logger.critical("Download called without specifying what to download!")
return ""
emf_logger.debug("in get_downloads: info={0}".format(info))
if info['download'] == 'file':
# there are only a certain number of fixed files that we want people to download
filename = info['download_file']
if filename == "web_modforms.py":
dirname = emf.app.root_static_folder
try:
emf_logger.debug("Dirname:{0}, Filename:{1}".format(dirname, filename))
return send_from_directory(dirname, filename, as_attachment=True, attachment_filename=filename)
except IOError:
info['error'] = "Could not find file! "
if info['download'] == 'coefficients':
info['tempfile'] = "/tmp/tmp_web_mod_form.txt"
return get_coefficients(info)
if info['download'] == 'object':
return download_web_modform(info)
info['error'] = "Could not find file! "
def connect_to_modularforms_db(collection="", create=True):
r"""
Return a handle to a modular forms database or a specific collection.
"""
db_name = "modularforms2"
try:
C = lmfdb.base.getDBConnection()
except Exception as e:
emf_logger.critical("Could not connect to Database! db={0}. Error: {1}".format(db_name, e.message))
try:
if collection != "":
return C[db_name][collection]
else:
return C[db_name]
except Exception as e:
if collection != "":
error_st = (
"Either Database %s does not exist or Collection %s is not in database %s at connection %s. Error: %s"
% (db_name, collection, db_name, C, e)
)
else:
error_st = "Database %s does not exist at connection %s. Error: %s" % (db_name, C, e)
raise ValueError, error_st
def WebNewForm_cached(level,weight,character,label,parent=None, **kwds):
if use_cache:
M = WebModFormSpace_cached(level, weight, character)
return M.hecke_orbits[label]
else:
F = WebNewForm(level,weight,character,label,**kwds)
emf_logger.critical("Computed F not using cache!")
return F
def WebNewForm_cached(level, weight, character, label, parent=None, **kwds):
if use_cache:
M = WebModFormSpace_cached(level, weight, character)
return M.hecke_orbits[label]
else:
F = WebNewForm(level, weight, character, label, **kwds)
emf_logger.critical("Computed F not using cache!")
return F
def first_nonvanishing_coefficient_trace(self):
if self._nv_coeff_trace is not None:
return self._nv_coeff_trace
try:
a = self.first_nonvanishing_coefficient()
self._nv_coeff_trace = a.trace()
return self._nv_coeff_trace
except AttributeError as e:
emf_logger.critical(e)
def first_nonvanishing_coefficient_norm(self):
if self._nv_coeff_norm is not None:
return self._nv_coeff_norm
try:
a = self.first_nonvanishing_coefficient()
self._nv_coeff_norm = a.norm()
return self._nv_coeff_norm
except AttributeError as e:
emf_logger.critical(e)
def first_nonvanishing_coefficient_norm(self):
if self._nv_coeff_norm is not None:
return self._nv_coeff_norm
try:
a = self.first_nonvanishing_coefficient()
self._nv_coeff_norm = a.norm()
return self._nv_coeff_norm
except AttributeError as e:
emf_logger.critical(e)
def first_nonvanishing_coefficient_trace(self):
if self._nv_coeff_trace is not None:
return self._nv_coeff_trace
try:
a = self.first_nonvanishing_coefficient()
self._nv_coeff_trace = a.trace()
return self._nv_coeff_trace
except AttributeError as e:
emf_logger.critical(e)
def extend_from_db(self):
setattr(self._value, "lmfdb_label", self._db_value)
if not self._db_value is None and self._db_value != '':
try:
url = url_for("number_fields.by_label", label=self._db_value)
except RuntimeError:
emf_logger.critical("could not set url for the label")
url = ''
setattr(self._value, "lmfdb_url",url)
setattr(self._value, "lmfdb_pretty", field_pretty(self._db_value))
else:
setattr(self._value, "lmfdb_pretty", web_latex_split_on_pm(self._value.absolute_polynomial()))
def extend_from_db(self):
setattr(self._value, "lmfdb_label", self._db_value)
if not self._db_value is None and self._db_value != '':
try:
url = url_for("number_fields.by_label", label=self._db_value)
except RuntimeError:
emf_logger.critical("could not set url for the label")
url = ''
setattr(self._value, "lmfdb_url", url)
setattr(self._value, "lmfdb_pretty", field_pretty(self._db_value))
else:
setattr(self._value, "lmfdb_pretty",
web_latex_split_on_pm(self._value.absolute_polynomial()))
def authorize(self):
r"""
Need to be authorized to insert data
"""
from lmfdb.base import getDBConnection
from os.path import dirname, join
pw_filename = join(dirname(dirname(__file__)), "password")
user = "******"
password = open(pw_filename, "r").readlines()[0].strip()
C = getDBConnection()
C["modularforms2"].authenticate(user, password)
emf_logger.critical("Authenticated with user:{0} and pwd:{1}".format(user, password))
def WebChar_cached(modulus, number, **kwds):
if use_cache:
label = "{0}.{1}".format(modulus, number)
X = cache.get(label)
emf_logger.critical("Looking for cached char:{0}".format(label))
if X is None:
emf_logger.debug("X was not in cache!")
X = WebChar(modulus, number, **kwds)
cache.set(label, X, timeout=5 * 60)
else:
emf_logger.critical("X was in cache!")
else:
X = WebChar(modulus, number, **kwds)
return X
def WebModFormSpace_cached(level, weight, character, **kwds):
if use_cache:
label = space_label(level, weight, character, make_cache_label=True)
M = cache.get(label)
emf_logger.critical("Looking for cached space:{0}".format(label))
if M is None:
emf_logger.debug("M was not in cache!")
M = WebModFormSpace(level, weight, character, **kwds)
cache.set(label, M, timeout=5 * 60)
else:
emf_logger.critical("M was in cache!")
else:
M = WebModFormSpace(level, weight, character, **kwds)
return M
def __init__(self, name, level, weight, character, parent=None, **kwds):
emf_logger.debug(
"Get Hecke orbits! {0},{1},{2},{3},{4},kwds={5}".format(
name, level, weight, character, type(parent), kwds))
self.level = level
self.weight = weight
self.character = character
self.parent = parent
super(WebHeckeOrbits, self).__init__(name,
None,
save_to_db=True,
save_to_fs=False,
**kwds)
emf_logger.critical("Initiated Hecke orbits!")
def WebChar_cached(modulus, number, **kwds):
if use_cache:
label = "{0}.{1}".format(modulus, number)
X = cache.get(label)
emf_logger.critical("Looking for cached char:{0}".format(label))
if X is None:
emf_logger.debug("X was not in cache!")
X = WebChar(modulus, number, **kwds)
cache.set(label, X, timeout=5 * 60)
else:
emf_logger.critical("X was in cache!")
else:
X = WebChar(modulus, number, **kwds)
return X
def get_files_from_gridfs(collection='',create=True):
r"""
Return a handle to a modular forms database or a specific collection.
"""
C = connect_to_modularforms_db()
if 'files' not in collection:
collection_name = collection + '.files'
else:
collection_name = collection.split('.')[0]
try:
return gridfs.GridFS(C,collection)
except Exception as e:
error_st = "Collection {0} is not in database {1} at connection {2}. Error: {3}".format(collection,db_name,C,e)
emf_logger.critical(error_st)
raise ValueError,error_st
def render_web_modform_space(level=None, weight=None, character=None, label=None, **kwds):
r"""
Render the webpage for a elliptic modular forms space.
"""
emf_logger.debug("In render_elliptic_modular_form_space kwds: {0}".format(kwds))
emf_logger.debug(
"Input: level={0},weight={1},character={2},label={3}".format(level, weight, character, label))
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
try:
info = set_info_for_modular_form_space(**info)
except RuntimeError as e:
errst = "The space {0}.{1}.{2} is not in the database!".format(level,weight,character)
flash(errst,'error')
info = {'error': ''}
emf_logger.debug("keys={0}".format(info.keys()))
if info.has_key('error'):
emf_logger.critical("error={0}".format(info['error']))
if 'download' in kwds and 'error' not in kwds:
return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
if 'dimension_newspace' in kwds and kwds['dimension_newspace'] == 1:
# if there is only one orbit we list it
emf_logger.debug("Dimension of newforms is one!")
info['label'] = 'a'
return redirect(url_for('emf.render_elliptic_modular_forms', **info))
if character>1:
info['title'] = "Newforms of weight %s for \(\Gamma_{0}(%s)\) with character \(\chi_{%s}(%s, \cdot)\)" % (weight, level, level, character)
else:
info['title'] = "Newforms of weight %s for \(\Gamma_{0}(%s)\)" % (weight, level)
bread = [(EMF_TOP, url_for('emf.render_elliptic_modular_forms'))]
bread.append(("Level %s" % level, url_for('emf.render_elliptic_modular_forms', level=level)))
bread.append(
("Weight %s" % weight, url_for('emf.render_elliptic_modular_forms', level=level, weight=weight)))
bread.append(
("Character \(\chi_{%s}(%s, \cdot)\)" % (level, character), url_for('emf.render_elliptic_modular_forms', level=level, weight=weight, character=character)))
# emf_logger.debug("friends={0}".format(friends))
info['bread'] = bread
info['learnmore'] = [('History of Modular forms', url_for('holomorphic_mf_history'))]
emf_logger.debug("info={0}".format(info))
if info.has_key('space'):
emf_logger.debug("space={0}".format(info['space']))
emf_logger.debug("dimension={0}".format(info['space'].dimension))
if info.has_key('error'):
emf_logger.debug("error={0}".format(info['error']))
return render_template("emf_web_modform_space.html", **info)
def render_web_modform_space(level=None, weight=None, character=None, label=None, **kwds):
r"""
Render the webpage for a elliptic modular forms space.
"""
emf_logger.debug("In render_elliptic_modular_form_space kwds: {0}".format(kwds))
emf_logger.debug(
"Input: level={0},weight={1},character={2},label={3}".format(level, weight, character, label))
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
try:
info = set_info_for_modular_form_space(**info)
except RuntimeError:
errst = "The space {0}.{1}.{2} is not in the database!".format(level,weight,character)
flash(errst,'error')
info = {'error': ''}
emf_logger.debug("keys={0}".format(info.keys()))
if info.has_key('error'):
emf_logger.critical("error={0}".format(info['error']))
if 'download' in kwds and 'error' not in kwds:
return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'], add_etags=False)
if 'dimension_newspace' in kwds and kwds['dimension_newspace'] == 1:
# if there is only one orbit we list it
emf_logger.debug("Dimension of newforms is one!")
info['label'] = 'a'
return redirect(url_for('emf.render_elliptic_modular_forms', **info))
if character>1:
info['title'] = "Newforms of weight %s for \(\Gamma_{0}(%s)\) with character \(\chi_{%s}(%s, \cdot)\)" % (weight, level, level, character)
else:
info['title'] = "Newforms of weight %s for \(\Gamma_{0}(%s)\)" % (weight, level)
bread = [(MF_TOP, url_for('mf.modular_form_main_page')), (EMF_TOP, url_for('emf.render_elliptic_modular_forms'))]
bread.append(("Level %s" % level, url_for('emf.render_elliptic_modular_forms', level=level)))
bread.append(
("Weight %s" % weight, url_for('emf.render_elliptic_modular_forms', level=level, weight=weight)))
bread.append(
("Character \(\chi_{%s}(%s, \cdot)\)" % (level, character), url_for('emf.render_elliptic_modular_forms', level=level, weight=weight, character=character)))
# emf_logger.debug("friends={0}".format(friends))
info['bread'] = bread
info['learnmore'] = [('History of modular forms', url_for('.holomorphic_mf_history'))]
emf_logger.debug("info={0}".format(info))
if info.has_key('space'):
emf_logger.debug("space={0}".format(info['space']))
emf_logger.debug("dimension={0}".format(info['space'].dimension))
if info.has_key('error'):
emf_logger.debug("error={0}".format(info['error']))
return render_template("emf_web_modform_space.html", **info)
def find(cls, query={}, projection=None, sort=[]):
r'''
Search the database using ```query``` and return
an iterator over the set of matching objects of this WebObject
'''
coll = cls.connect_to_db(cls._collection_name)
for s in coll.find(query, sort=sort, projection=projection):
s.pop('_id')
try:
k = {key: s[key] for key in cls._key}
o = cls(update_from_db=False, **k)
o.update_db_properties_from_dict(s)
yield o
except KeyError as e:
emf_logger.critical(
"Malformed data in the database {}, {}".format(e, s))
continue
def get_files_from_gridfs(collection="", create=True):
r"""
Return a handle to a modular forms database or a specific collection.
"""
C = connect_to_modularforms_db()
# FIXME collection_name is set but never used
# if 'files' not in collection:
# collection_name = collection + '.files'
# else:
# collection_name = collection.split('.')[0]
try:
return gridfs.GridFS(C, collection)
except Exception as e:
error_st = "Collection {0} is not in database {1}. Error: {2}".format(collection, C, e)
emf_logger.critical(error_st)
raise ValueError, error_st
def save_to_db(self, update=True):
r"""
Saves ```self``` to the database, i.e.
save the meta record and the file in the gridfs file system.
"""
import pymongo
from pymongo.errors import OperationFailure
fs = self._files
try:
self.authorize()
except OperationFailure:
emf_logger.critical(
"Authentication failed. You are not authorized to save data to the database!"
)
return False
if self._use_gridfs:
file_key = self.file_key_dict()
coll = self._file_collection
if fs.exists(file_key):
emf_logger.debug("File exists with key={0}".format(file_key))
if not update:
return True
else:
fid = coll.find_one(file_key, projection=['_id'])['_id']
fs.delete(fid)
emf_logger.debug("Deleted file with fid={0}".format(fid))
# insert
s = dumps(self.fs_dict())
if not self._use_separate_db:
file_key.update(self.db_dict())
try:
t = fs.put(s, **file_key)
emf_logger.debug("Inserted file with filekey={1}".format(
t, file_key))
except Exception, e:
emf_logger.debug(
"Could not insert file with filekey={1}".format(
s, file_key))
emf_logger.warn("Error inserting record: {0}".format(e))
#fid = coll.find_one(key)['_id']
# insert extended record
if not self._use_separate_db:
self.logout()
return True
def find(cls, query={}, projection = None, sort=[], gridfs_only=False):
r'''
Search the database using ```query``` and return
an iterator over the set of matching objects of this WebObject
'''
if gridfs_only: # stupid hack, should be a property of the class or standard that way
coll = cls.connect_to_db(cls._collection_name).files
else:
coll = cls.connect_to_db(cls._collection_name)
for s in coll.find(query, sort=sort, projection=projection):
s.pop('_id')
try:
k = {key:s[key] for key in cls._key}
o = cls(update_from_db=False, init_dynamic_properties=False, **k)
o.update_db_properties_from_dict(s)
yield o
except KeyError as e:
emf_logger.critical("Malformed data in the database {}, {}".format(e,s))
continue
def find(cls, query={}, projection = None, sort=[], gridfs_only=False):
r'''
Search the database using ```query``` and return
an iterator over the set of matching objects of this WebObject
'''
if gridfs_only: # stupid hack, should be a property of the class or standard that way
coll = cls.connect_to_db(cls._collection_name).files
else:
coll = cls.connect_to_db(cls._collection_name)
for s in coll.find(query, sort=sort, projection=projection):
s.pop('_id')
try:
k = {key:s[key] for key in cls._key}
o = cls(update_from_db=False, init_dynamic_properties=False, **k)
o.update_db_properties_from_dict(s)
yield o
except KeyError as e:
emf_logger.critical("Malformed data in the database {}, {}".format(e,s))
continue
def extend_from_db(self):
setattr(self._value, "lmfdb_label", self._db_value)
if not self._db_value is None and self._db_value != '':
label = self._db_value
setattr(self._value, "lmfdb_pretty", field_pretty(label))
else:
if self._value.absolute_degree() == 1:
label = '1.1.1.1'
setattr(self._value, "lmfdb_pretty", field_pretty(label))
setattr(self._value, "lmfdb_label", label)
else:
emf_logger.critical("could not set lmfdb_pretty for the label")
label = ''
if label != '':
try:
url = url_for("number_fields.by_label", label=label)
setattr(self._value, "lmfdb_url", url)
except RuntimeError:
emf_logger.critical("could not set url for the label")
def extend_from_db(self):
setattr(self._value, "lmfdb_label", self._db_value)
if not self._db_value is None and self._db_value != '':
label = self._db_value
setattr(self._value, "lmfdb_pretty", field_pretty(label))
else:
if self._value == QQ:
label = '1.1.1.1'
setattr(self._value, "lmfdb_pretty", field_pretty(label))
setattr(self._value, "lmfdb_label", label)
else:
emf_logger.critical("could not set lmfdb_pretty for the label")
label = ''
if label != '':
try:
url = url_for("number_fields.by_label", label=label)
setattr(self._value, "lmfdb_url", url)
except RuntimeError:
emf_logger.critical("could not set url for the label")
def from_db(self, l):
emf_logger.critical("Get Hecke orbits for labels : {0}!".format(l))
from lmfdb.modular_forms.elliptic_modular_forms.backend.web_newforms import WebNewForm_cached, WebNewForm
res = {}
for lbl in l:
F = WebNewForm(self.level,
self.weight,
self.character,
lbl,
parent=self.parent)
#F = WebNewForm_cached(self.level, self.weight, self.character, lbl, parent=self.parent)
emf_logger.debug("Got F for label {0} : {1}".format(lbl, F))
res[lbl] = F
# return {lbl : WebNewForm_cached(self.level, self.weight, self.character, lbl, parent=self.parent)
# for lbl in l}
emf_logger.critical("Got Hecke orbits!")
return res
def __init__(self, group=0):
self._group = group
self._table = dict()
db = connect_db()
dims = db['dimensions']
emf_logger.debug('group={0}'.format(group))
try:
if group == 0:
rec = dims.find_one({'group': 'gamma0'})
self.dimension = self.dimension_gamma0
# emf_logger.debug('rec={0}'.format(rec))
elif group == 1:
rec = dims.find_one({'group': 'gamma1'})
self.dimension = self.dimension_gamma1
except:
emf_logger.critical('Critical error: No dimension information for group={0}'.format(group))
if rec:
self._table = loads(rec['data'])
else:
self._table = None
def __init__(self, group=0):
self._group = group
self._table = dict()
db = connect_db()
dims = db['dimensions']
emf_logger.debug('group={0}'.format(group))
try:
if group == 0:
rec = dims.find_one({'group': 'gamma0'})
self.dimension = self.dimension_gamma0
# emf_logger.debug('rec={0}'.format(rec))
elif group == 1:
rec = dims.find_one({'group': 'gamma1'})
self.dimension = self.dimension_gamma1
except:
emf_logger.critical('Critical error: No dimension information for group={0}'.format(group))
if rec:
self._table = loads(rec['data'])
else:
self._table = None
def connect_to_modularforms_db(collection='',create=True):
r"""
Return a handle to a modular forms database or a specific collection.
"""
db_name = 'modularforms2'
try:
C = lmfdb.base.getDBConnection()
except Exception as e:
emf_logger.critical("Could not connect to Database! db={0}. Error: {1}".format(db_name,e.message))
try:
if collection != '':
return C[db_name][collection]
else:
return C[db_name]
except Exception as e:
if collection != '':
error_st = "Either Database %s does not exist or Collection %s is not in database %s at connection %s. Error: %s" % (db_name, collection, db_name, C,e);
else:
error_st = "Database %s does not exist at connection %s. Error: %s" % (db_name, C,e);
raise ValueError,error_st
def __init__(self, group=0):
self._group = group
self._table = dict()
db = connect_db()
dims = db["dimensions"]
emf_logger.debug("dims table ={0}".format(dims))
emf_logger.debug("group={0}".format(group))
try:
if group == 0:
rec = dims.find_one({"group": "gamma0"})
self.dimension = self.dimension_gamma0
emf_logger.debug("rec={0}".format(rec["_id"]))
elif group == 1:
rec = dims.find_one({"group": "gamma1"})
self.dimension = self.dimension_gamma1
except:
rec = None
emf_logger.critical("Critical error: No dimension information for group={0}".format(group))
if rec <> None:
self._table = loads(rec["data"])
else:
self._table = None
emf_logger.debug("Have information for levels {0}".format(self._table.keys()))
def render_fd_plot(level, info, **kwds):
group = None
grouptype = None
if ('group' in info):
group = info['group']
# we only allow standard groups
if 'grouptype' in info:
grouptype = int(info['grouptype'])
if info['grouptype'] == 0:
group = 'Gamma0'
elif info['grouptype'] == 1:
group = 'Gamma1'
if (group not in ['Gamma0', 'Gamma', 'Gamma1']):
group = 'Gamma0'
grouptype = int(0)
else:
if grouptype is None:
if group == 'Gamma':
grouptype = int(-1)
elif group == 'Gamma0':
grouptype = int(0)
else:
grouptype = int(1)
db_name = 'SL2Zsubgroups'
collection = 'groups'
C = lmfdb.base.getDBConnection()
emf_logger.debug("C={0}, level={1}, grouptype={2}".format(
C, level, grouptype))
if not C:
emf_logger.critical("Could not connect to Database! C={0}".format(C))
if not db_name in C.database_names():
emf_logger.critical(
"Incorrect database name {0}. \n Available databases are:{1}".
format(db_name, C.database_names()))
if not collection in C[db_name].collection_names():
emf_logger.critical(
"Incorrect collection {0} in database {1}. \n Available collections are:{2}"
.format(collection, db_name, C[db_name].collection_names()))
find = C[db_name][collection].find_one({
'level': int(level),
'type': int(grouptype)
})
if find:
if find.get('domain'):
# domain=loads(str(find['domain']))
domain = find['domain']
emf_logger.debug('Found fundamental domain in database')
else:
emf_logger.debug(
'Drawing fundamental domain for group {0}({1})'.format(
group, level))
domain = draw_fundamental_domain(level, group, **kwds)
# G=Gamma0(level)
# C[db_name][collection].insert({'level':int(level), 'type':type, 'index':int(G.index), 'G':bson.binary.Binary(dumps(G)), 'domain': bson.binary.Binary(dumps(domain))})
# emf_logger.debug('Inserting group and fundamental domain in database')
return domain
def __init__(self, group=0):
self._group = group
self._table = dict()
db = connect_db()
dims = db['dimensions']
emf_logger.debug('dims table ={0}'.format(dims))
emf_logger.debug('group={0}'.format(group))
try:
if group == 0:
rec = dims.find_one({'group': 'gamma0'})
self.dimension = self.dimension_gamma0
emf_logger.debug('rec={0}'.format(rec['_id']))
elif group == 1:
rec = dims.find_one({'group': 'gamma1'})
self.dimension = self.dimension_gamma1
except:
rec = None
emf_logger.critical('Critical error: No dimension information for group={0}'.format(group))
if rec<>None:
self._table = loads(rec['data'])
else:
self._table = None
if self._table <> None:
emf_logger.debug('Have information for levels {0}'.format(self._table.keys()))
def __init__(self,
modulus=1,
number=1,
update_from_db=True,
compute=False):
r"""
Init self.
"""
emf_logger.critical("In WebChar {0}".format(
(modulus, number, update_from_db, compute)))
if not gcd(number, modulus) == 1:
raise ValueError, "Character number {0} of modulus {1} does not exist!".format(
number, modulus)
if number > modulus:
number = number % modulus
self._properties = WebProperties(
WebInt('conductor'), WebInt('modulus', value=modulus),
WebInt('number', value=number), WebInt('modulus_euler_phi'),
WebInt('order'), WebStr('latex_name'),
WebStr('label', value="{0}.{1}".format(modulus, number)),
WebNoStoreObject('sage_character', type(trivial_character(1))),
WebDict('_values_algebraic'), WebDict('_values_float'),
WebDict('_embeddings'),
WebFloat('version', value=float(emf_version)))
emf_logger.debug('Set properties in WebChar!')
super(WebChar, self).__init__(update_from_db=update_from_db)
if self._has_updated_from_db is False:
self.init_dynamic_properties(
) # this was not done if we exited early
compute = True
if compute:
self.compute(save=True)
#emf_logger.debug('In WebChar, self.__dict__ = {0}'.format(self.__dict__))
emf_logger.debug('In WebChar, self.number = {0}'.format(self.number))
def render_fd_plot(level, info, **kwds):
group = None
grouptype = None
if('group' in info):
group = info['group']
# we only allow standard groups
if 'grouptype' in info:
grouptype = int(info['grouptype'])
if info['grouptype'] == 0:
group = 'Gamma0'
elif info['grouptype'] == 1:
group = 'Gamma1'
if (group not in ['Gamma0', 'Gamma', 'Gamma1']):
group = 'Gamma0'
grouptype = int(0)
else:
if grouptype is None:
if group == 'Gamma':
grouptype = int(-1)
elif group == 'Gamma0':
grouptype = int(0)
else:
grouptype = int(1)
db_name = 'SL2Zsubgroups'
collection = 'groups'
C = lmfdb.base.getDBConnection()
emf_logger.debug("C={0}, level={1}, grouptype={2}".format(C, level, grouptype))
if not C:
emf_logger.critical("Could not connect to Database! C={0}".format(C))
if not db_name in C.database_names():
emf_logger.critical("Incorrect database name {0}. \n Available databases are:{1}".format(
db_name, C.database_names()))
if not collection in C[db_name].collection_names():
emf_logger.critical("Incorrect collection {0} in database {1}. \n Available collections are:{2}".format(collection, db_name, C[db_name].collection_names()))
find = C[db_name][collection].find_one({'level': int(level), 'type': int(grouptype)})
if find:
if find.get('domain'):
# domain=loads(str(find['domain']))
domain = find['domain']
emf_logger.debug('Found fundamental domain in database')
else:
emf_logger.debug('Drawing fundamental domain for group {0}({1})'.format(group, level))
domain = draw_fundamental_domain(level, group, **kwds)
# G=Gamma0(level)
# C[db_name][collection].insert({'level':int(level), 'type':type, 'index':int(G.index), 'G':bson.binary.Binary(dumps(G)), 'domain': bson.binary.Binary(dumps(domain))})
# emf_logger.debug('Inserting group and fundamental domain in database')
return domain
def set_info_for_modular_form_space(level=None, weight=None, character=None, label=None, **kwds):
r"""
Set information about a space of modular forms.
"""
info = dict()
info["level"] = level
info["weight"] = weight
info["character"] = character
emf_logger.debug("info={0}".format(info))
# DB = connect_to_modularforms_db()
# if level <> None and weight <> None and character <> None:
# s = {'N':int(level),'k':int(weight),'chi':int(character)}
# if DB.Newform_factors.files.find(s).count()==0:
#
# if(level > N_max_db or weight > k_max_db):
# info['error'] = "Currently not available"
#
WMFS = None
if level <= 0:
info["error"] = "Got wrong level: %s " % level
return info
try:
WMFS = WebModFormSpace(N=level, k=weight, chi=character)
if "download" in info and "tempfile" in info:
WNF._save_to_file(info["tempfile"])
info["filename"] = str(weight) + "-" + str(level) + "-" + str(character) + "-" + label + ".sobj"
return info
except Exception as e:
if isinstance(e, IndexError):
info["error"] = e.message
WMFS = None
if WMFS == None:
info["error"] = "We are sorry. The sought space can not be found in the database."
return info
if WMFS.level() == 1:
info["group"] = "\( \mathrm{SL}_{2}(\mathbb{Z})\)"
else:
info["group"] = "\( \Gamma_{{0}}( {0} ) \)".format(WMFS.level())
if character == 0:
info["name_new"] = "\(S_{ %s }^{new}(%s) \)" % (WMFS.weight(), WMFS.level())
info["name_old"] = "\(S_{ %s }^{old}(%s) \)" % (WMFS.weight(), WMFS.level())
else:
conrey_char = WMFS.conrey_character()
conrey_char_name = WMFS.conrey_character_name()
info["conrey_character_name"] = "\( " + conrey_char_name + "\)"
info["character_url"] = url_for(
"characters.render_Dirichletwebpage", modulus=WMFS.level(), number=conrey_char.number()
)
info["name_new"] = "\(S_{ %s }^{new}(%s,%s) \)" % (WMFS.weight(), WMFS.level(), conrey_char_name)
info["name_old"] = "\(S_{ %s }^{old}(%s,%s) \)" % (WMFS.weight(), WMFS.level(), conrey_char_name)
info["dimension_cusp_forms"] = WMFS.dimension_cusp_forms()
info["dimension_mod_forms"] = WMFS.dimension_modular_forms()
info["dimension_new_cusp_forms"] = WMFS.dimension_new_cusp_forms()
info["dimension_newspace"] = WMFS.dimension_newspace()
info["dimension_oldspace"] = WMFS.dimension_oldspace()
info["dimension"] = WMFS.dimension()
info["galois_orbits"] = WMFS.get_all_galois_orbit_info()
lifts = list()
if WMFS.dimension() == 0: # we don't need to work with an empty space
info["sturm_bound"] = 0
info["new_decomposition"] = ""
info["is_empty"] = 1
lifts.append(("Half-Integral Weight Forms", "/ModularForm/Mp2/Q"))
lifts.append(("Siegel Modular Forms", "/ModularForm/GSp4/Q"))
info["lifts"] = lifts
return info
info["sturm_bound"] = WMFS.sturm_bound()
info["new_decomposition"] = WMFS.print_galois_orbits()
emf_logger.debug("new_decomp={0}".format(info["new_decomposition"]))
info["nontrivial_new"] = len(info["new_decomposition"])
if info["new_decomposition"] == "":
if info["dimension_newspace"] > 0:
info["nontrivial_new_info"] = " is unfortunately not in the database yet!"
else:
info["nontrivial_new_info"] = " is empty!"
## we try to catch well-known bugs...
info["old_decomposition"] = "n/a"
if level < N_max_comp:
try:
O = WMFS.print_oldspace_decomposition()
info["old_decomposition"] = O
except:
emf_logger.critical("Error in computing oldspace decomposition")
O = []
info["old_decomposition"] = ""
(A, B, C) = sys.exc_info()
# build an error message...
errtype = A.__name__
errmsg = B
s = "%s: %s at:" % (errtype, errmsg)
next = C.tb_next
while next:
ln = next.tb_lineno
filen = next.tb_frame.f_code.co_filename
s += "\n line no. %s in file %s" % (ln, filen)
next = next.tb_next
info["error_note"] = "Could not construct oldspace!\n" + s
# properties for the sidebar
prop = []
if WMFS._cuspidal == 1:
prop = [("Dimension newforms", [info["dimension_newspace"]])]
prop.append(("Dimension oldforms", [info["dimension_oldspace"]]))
else:
prop = [("Dimension modular forms", [info["dimension_mod_forms"]])]
prop.append(("Dimension cusp forms", [info["dimension_cusp_forms"]]))
prop.append(("Sturm bound", [WMFS.sturm_bound()]))
info["properties2"] = prop
## Make parent spaces of S_k(N,chi) for the sidebar
par_lbl = "\( S_{*} (\Gamma_0(" + str(level) + "),\cdot )\)"
par_url = "?level=" + str(level)
parents = [[par_lbl, par_url]]
par_lbl = "\( S_{k} (\Gamma_0(" + str(level) + "),\cdot )\)"
par_url = "?level=" + str(level) + "&weight=" + str(weight)
parents.append((par_lbl, par_url))
info["parents"] = parents
if "character" in info:
info["character_order"] = WMFS.character_order()
info["character_conductor"] = WMFS.character_conductor()
friends = list()
lifts = list()
if ("label" not in info) and info["old_decomposition"] != "n/a":
O = WMFS.oldspace_decomposition()
try:
for (old_level, chi, mult, d) in O:
if chi != 0:
s = "\(S_{%s}(\Gamma_0(%s),\chi_{%s}) \) " % (weight, old_level, chi)
friends.append(
(s, "?weight=" + str(weight) + "&level=" + str(old_level) + "&character=" + str(chi))
)
else:
s = "\(S_{%s}(\Gamma_0(%s)) \) " % (weight, old_level)
friends.append((s, "?weight=" + str(weight) + "&level=" + str(old_level) + "&character=" + str(0)))
except:
pass
info["friends"] = friends
lifts.append(("Half-Integral Weight Forms", "/ModularForm/Mp2/Q"))
lifts.append(("Siegel Modular Forms", "/ModularForm/GSp4/Q"))
info["lifts"] = lifts
# emf_logger.debug("Info = {0}".format(info))
return info
def emf_error(s):
s = "ERROR: " + s
s = "<span style='color:red;'>{0}</span>".format(s)
emf_logger.critical(s)
return s
from lmfdb.utils import to_dict, image_src
from sage.all import dimension_new_cusp_forms, dimension_cusp_forms, dimension_eis, dimension_modular_forms, Zmod, DirichletGroup, latex
from lmfdb.modular_forms.elliptic_modular_forms import EMF, emf_logger, emf, EMF_TOP, N_max_Gamma0_fdraw, N_max_Gamma1_fdraw
from lmfdb.modular_forms.elliptic_modular_forms.backend.emf_core import get_geometric_data
from lmfdb.modular_forms.elliptic_modular_forms.backend.emf_utils import my_get, parse_range, extract_limits_as_tuple
from lmfdb.modular_forms.backend.mf_utils import my_get
from lmfdb.modular_forms import MF_TOP
from lmfdb.modular_forms.elliptic_modular_forms import N_max_comp, k_max_comp, N_max_db, k_max_db
from flask import render_template, url_for, request, redirect, make_response, send_file
from lmfdb.modular_forms.elliptic_modular_forms.backend.emf_classes import ClassicalMFDisplay, DimensionTable
list_of_implemented_dims = ['new', 'cusp', 'modular', 'eisenstein']
try:
from dirichlet_conrey import *
except:
emf_logger.critical("Could not import dirichlet_conrey!")
met = ['POST', 'GET']
@emf.route("/TablesMF/", methods=met)
@emf.route("/TablesMF/<int:nrows>/<int:ncols>/", methods=met)
def draw_table(nrows=None, ncols=None, **kwds):
if request.method == 'GET':
info = to_dict(request.args)
else:
info = to_dict(request.form)
ncols = my_get(info, 'ncols', ncols, int)
nrows = my_get(info, 'nrows', nrows, int)
if nrows is None or ncols is None:
return emf_error("Please supply level weight (and optional character)!"), 500
def set_info_for_web_newform(level=None, weight=None, character=None, label=None, **kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'bprec', default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm_cached(level=level, weight=weight, character=character, label=label)
if not WNF.has_updated():
raise IndexError("Unfortunately, we do not have this newform in the database.")
info['character_order'] = WNF.character.order
info['code'] = WNF.code
emf_logger.debug("defined webnewform for rendering!")
except IndexError as e:
info['error'] = e.message
url0 = url_for("mf.modular_form_main_page")
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
bread = [(MF_TOP, url0), (EMF_TOP, url1)]
bread.append(("Level %s" % level, url2))
bread.append(("Weight %s" % weight, url3))
bread.append(("Character \( %s \)" % (WNF.character.latex_name), url4))
bread.append(("Newform %d.%d.%d.%s" % (level, weight, int(character), label),''))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',level=level, weight=weight, character=character)
friends.append(('\( S_{%s}(%s, %s)\)'%(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if hasattr(WNF.base_ring, "lmfdb_url") and WNF.base_ring.lmfdb_url:
friends.append(('Number field ' + WNF.base_ring.lmfdb_pretty, WNF.base_ring.lmfdb_url))
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_label:
friends.append(('Number field ' + WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_url))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)", WNF.character.url()))
if WNF.dimension==0 and not info.has_key('error'):
info['error'] = "This space is empty!"
info['title'] = 'Newform ' + WNF.hecke_orbit_label
info['learnmore'] = [('History of modular forms', url_for('.holomorphic_mf_history'))]
if 'error' in info:
return info
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
## Example to illustrate the different cases
## base = CyclotomicField(n) -- of degree phi(n)
## coefficient_field = NumberField( p(x)) for some p in base['x'] of degree m
## we would then have cdeg = m*phi(n) and bdeg = phi(n)
## and rdeg = m
## Unfortunately, for e.g. base = coefficient_field = CyclotomicField(6)
## we get coefficient_field.relative_degree() == 2 although it should be 1
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if cdeg == 1:
rdeg = 1
else:
## just setting rdeg = WNF.coefficient_field.relative_degree() does not give correct result...
##
rdeg = QQ(cdeg)/QQ(bdeg)
cf_is_QQ = (cdeg == 1)
br_is_QQ = (bdeg == 1)
if cf_is_QQ:
info['satake'] = WNF.satake
if WNF.complexity_of_first_nonvanishing_coefficients() > default_max_height:
info['qexp'] = ""
info['qexp_display'] = ''
info['hide_qexp'] = True
n,c = WNF.first_nonvanishing_coefficient()
info['trace_nv'] = latex(WNF.first_nonvanishing_coefficient_trace())
info['norm_nv'] = '\\approx ' + latex(WNF.first_nonvanishing_coefficient_norm().n())
info['index_nv'] = n
else:
if WNF.prec < prec:
#get WNF record at larger prec
WNF.prec = prec
WNF.update_from_db()
info['qexp'] = WNF.q_expansion_latex(prec=10, name='\\alpha ')
info['qexp_display'] = url_for(".get_qexp_latex", level=level, weight=weight, character=character, label=label)
info["hide_qexp"] = False
info['max_cn_qexp'] = WNF.q_expansion.prec()
## All combinations should be tested...
## 13/4/4/a -> base ring = coefficient_field = QQ(zeta_6)
## 13/3/8/a -> base_ring = QQ(zeta_4), coefficient_field has poly x^2+(2\zeta_4+2x-3\zeta_$ over base_ring
## 13/4/3/a -> base_ring = coefficient_field = QQ(zeta_3)
## 13/4/1/a -> all rational
## 13/6/1/a/ -> base_ring = QQ, coefficient_field = Q(sqrt(17))
## These are variables which needs to be set properly below
info['polvars'] = {'base_ring':'x','coefficient_field':'\\alpha'}
if not cf_is_QQ:
if rdeg>1: # not WNF.coefficient_field == WNF.base_ring:
## Here WNF.base_ring should be some cyclotomic field and we have an extension over this.
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1, '\\alpha') # make the variable \alpha
c_pol_ltx_x = web_latex_poly(p1, 'x')
zeta = p1.base_ring().gens()[0]
# p2 = zeta.minpoly() #this is not used anymore
# b_pol_ltx = web_latex_poly(p2, latex(zeta)) #this is not used anymore
z1 = zeta.multiplicative_order()
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'),c_pol_ltx_x, z1]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).</div><br/>'.format(c_pol_ltx)
info['polvars']['base_ring']='i'
elif z1<=2:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(c_pol_ltx)
else:
info['polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\) '%(c_pol_ltx, z1,z1)
info['polvars']['base_ring']='\zeta_{{ {0} }}'.format(z1)
if z1==3:
info['polynomial_st'] += 'is a primitive cube root of unity.'
else:
info['polynomial_st'] += 'is a primitive {0}-th root of unity.'.format(z1)
elif not br_is_QQ:
## Now we have base and coefficient field being equal, meaning that since the coefficient field is not QQ it is some cyclotomic field
## generated by some \zeta_n
p1 = WNF.coefficient_field.absolute_polynomial()
z1 = WNF.coefficient_field.gens()[0].multiplicative_order()
c_pol_ltx = web_latex_poly(p1, '\\zeta_{{{0}}}'.format(z1))
c_pol_ltx_x = web_latex_poly(p1, 'x')
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'), c_pol_ltx_x]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where \(\zeta_4=e^{{\\frac{{\\pi i}}{{ 2 }} }}=i \).</div>'.format(c_pol_ltx)
info['polvars']['coefficient_field']='i'
elif z1<=2:
info['polynomial_st'] = ''
else:
info['polynomial_st'] = '<div class="where">where \(\zeta_{{{0}}}=e^{{\\frac{{2\\pi i}}{{ {0} }} }}\) '.format(z1)
info['polvars']['coefficient_field']='\zeta_{{{0}}}'.format(z1)
if z1==3:
info['polynomial_st'] += 'is a primitive cube root of unity.</div>'
else:
info['polynomial_st'] += 'is a primitive {0}-th root of unity.</div>'.format(z1)
else:
info['polynomial_st'] = ''
if info["hide_qexp"]:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg==1:
info['is_rational'] = 1
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty ]
else:
info['is_rational'] = 0
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings['values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = [('Level', str(level)),
('Weight', str(weight)),
('Character', '$' + WNF.character.latex_name + '$'),
('Label', WNF.hecke_orbit_label),
('Dimension of Galois orbit', str(WNF.dimension))]
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'], list) and len(info['twist_info'])>0:
info['is_minimal'] = info['twist_info'][0]
if(info['twist_info'][0]):
s = 'Is minimal<br>'
else:
s = 'Is a twist of lower level<br>'
properties2 += [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 += [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm == 1:
info['cm_field'] = "2.0.{0}.1".format(-WNF.cm_disc)
info['cm_disc'] = WNF.cm_disc
info['cm_field_knowl'] = nf_display_knowl(info['cm_field'], getDBConnection(), field_pretty(info['cm_field']))
info['cm_field_url'] = url_for("number_fields.by_label", label=info["cm_field"])
if WNF.is_cm is None or WNF.is_cm==-1:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm == 1:
s = 'Yes<br>'
else:
s = 'No<br>'
properties2.append(('CM', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev,dict) and len(alev.keys())>0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if(level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6','')
if poly != '':
d,monom,coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(len(coeffs)):
c = QQ(coeffs[i])
s = ""
if d>1 and i >0 and c>0:
s="+"
if c<0:
s="-"
if c.denominator()>1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(abs(c.numerator()),c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]; b = monom[i][1]
if a == 0 and b != 0:
s+="E_6^{{ {0} }}".format(b)
elif b ==0 and a != 0:
s+="E_4^{{ {0} }}".format(a)
else:
s+="E_4^{{ {0} }}E_6^{{ {1} }}".format(a,b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
# cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + '&label=' + str(label) # never used
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if(label_other != label):
s = 'Modular form '
if character:
s += newform_label(level,weight,character,label_other)
else:
s += newform_label(level,weight,1,label_other)
url = url_for('emf.render_elliptic_modular_forms', level=level,
weight=weight, character=character, label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s += newform_label(level,weight,character,label)
else:
s += newform_label(level,weight,1,label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for(
'emf.render_elliptic_modular_forms', level=level, weight=weight, character=character, label=label)
if WNF.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_degree):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight == 2 and WNF.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_available_prec()
return info
def __init__(self,
level=1,
weight=12,
character=1,
label='a',
prec=None,
parent=None,
update_from_db=True):
emf_logger.critical("In WebNewForm {0}".format(
(level, weight, character, label, parent, update_from_db)))
self._reduction = (type(self), (level, weight, character, label), {
'parent': parent,
'update_from_db': update_from_db
})
if isinstance(character, WebChar):
character_number = character.number
else:
character_number = character
character = None if parent is None else parent.character
if not isinstance(label, basestring):
if isinstance(label, (int, Integer)):
label = orbit_label(label)
else:
raise ValueError, "Need label either string or integer! We got:{0}".format(
label)
emf_logger.critical("Before init properties 0")
self._properties = WebProperties(
WebInt('level', value=level), WebInt('weight', value=weight),
WebCharProperty(
'character',
modulus=level,
number=character_number,
value=character,
include_in_update=True if character is None else False),
WebStr('character_naming_scheme', value='Conrey'),
WebStr('hecke_orbit_label',
default_value=newform_label(level, weight, character_number,
label)),
WebStr('label', default_value=label), WebInt('dimension'),
WebqExp('q_expansion'), WebDict('_coefficients'),
WebDict('_embeddings'), WebInt('prec', value=0),
WebNumberField('base_ring'), WebNumberField('coefficient_field'),
WebInt('coefficient_field_degree'),
WebList('twist_info', required=False),
WebBool('is_cm', required=False),
WebDict('_cm_values', required=False),
WebBool('is_cuspidal', default_value=True),
WebDict('satake', required=False),
WebDict('_atkin_lehner_eigenvalues', required=False),
WebBool('is_rational'), WebPoly('absolute_polynomial'),
WebFloat('version', value=float(emf_version), save_to_fs=True),
WebDict('explicit_formulas', required=False),
WebModFormSpaceProperty('parent',
value=parent,
level=level,
weight=weight,
character=character_number,
update_hecke_orbits=False)
# include_in_update = True if parent is None
# else False),
)
emf_logger.critical("After init properties 1")
super(WebNewForm, self).__init__(update_from_db=update_from_db)
emf_logger.critical("After init properties 2 prec={0}".format(
self.prec))
# We're setting the WebEigenvalues property after calling __init__ of the base class
# because it will set hecke_orbit_label from the db first
##
## We don't init the eigenvalues (since E*v is slow)
## unless we (later) request a coefficient which is not
## in self._coefficients
self.eigenvalues = WebEigenvalues(self.hecke_orbit_label,
prec=self.prec,
init_dynamic_properties=False)
emf_logger.critical("After init properties 3")
def set_info_for_modular_form_space(level=None, weight=None, character=None, label=None, **kwds):
r"""
Set information about a space of modular forms.
"""
info = dict()
info['level'] = level
info['weight'] = weight
info['character'] = character
emf_logger.debug("info={0}".format(info))
if(level > N_max_db or weight > k_max_db):
info['error'] = "Currently not available"
WMFS = None
if level <= 0:
info['error'] = "Got wrong level: %s " % level
return info
try:
if use_db:
WMFS = WebModFormSpace(weight, level, character, use_db=True)
else:
WMFS = WebModFormSpace(weight, level, character)
if 'download' in info and 'tempfile' in info:
WNF._save_to_file(info['tempfile'])
info['filename'] = str(weight) + '-' + str(level) + '-' + str(character) + '-' + label + '.sobj'
return info
except RuntimeError:
info['error'] = "Sage error: Could not construct the desired space!"
if WMFS.level() == 1:
info['group'] = "\( \mathrm{SL}_{2}(\mathbb{Z})\)"
else:
info['group'] = "\( \Gamma_{{0}}( {0} ) \)".format(WMFS.level())
if character == 0:
info['name_new'] = "\(S_{ %s }^{new}(%s) \)" % (WMFS.weight(), WMFS.level())
info['name_old'] = "\(S_{ %s }^{old}(%s) \)" % (WMFS.weight(), WMFS.level())
else:
conrey_char = WMFS.conrey_character()
conrey_char_name = WMFS.conrey_character_name()
info['conrey_character_name'] = '\( ' + conrey_char_name + '\)'
info['character_url'] = url_character(type='Dirichlet', modulus=WMFS.level(), number=conrey_char.number())
info['name_new'] = "\(S_{ %s }^{new}(%s,%s) \)" % (WMFS.weight(), WMFS.level(), conrey_char_name)
info['name_old'] = "\(S_{ %s }^{old}(%s,%s) \)" % (WMFS.weight(), WMFS.level(), conrey_char_name)
info['dimension_cusp_forms'] = WMFS.dimension_cusp_forms()
info['dimension_mod_forms'] = WMFS.dimension_modular_forms()
info['dimension_new_cusp_forms'] = WMFS.dimension_new_cusp_forms()
info['dimension_newspace'] = WMFS.dimension_newspace()
info['dimension_oldspace'] = WMFS.dimension_oldspace()
info['dimension'] = WMFS.dimension()
info['galois_orbits'] = WMFS.get_all_galois_orbit_info()
lifts = list()
if WMFS.dimension() == 0: # we don't need to work with an empty space
info['sturm_bound'] = 0
info['new_decomposition'] = ''
info['is_empty'] = 1
lifts.append(('Half-Integral Weight Forms', '/ModularForm/Mp2/Q'))
lifts.append(('Siegel Modular Forms', '/ModularForm/GSp4/Q'))
info['lifts'] = lifts
return info
info['sturm_bound'] = WMFS.sturm_bound()
info['new_decomposition'] = WMFS.print_galois_orbits()
emf_logger.debug("new_decomp={0}".format(info['new_decomposition']))
info['nontrivial_new'] = len(info['new_decomposition'])
## we try to catch well-known bugs...
info['old_decomposition'] = "n/a"
if level < N_max_comp:
try:
O = WMFS.print_oldspace_decomposition()
info['old_decomposition'] = O
except:
emf_logger.critical("Error in computing oldspace decomposition")
O = []
info['old_decomposition'] = "n/a"
(A, B, C) = sys.exc_info()
# build an error message...
errtype = A.__name__
errmsg = B
s = "%s: %s at:" % (errtype, errmsg)
next = C.tb_next
while(next):
ln = next.tb_lineno
filen = next.tb_frame.f_code.co_filename
s += "\n line no. %s in file %s" % (ln, filen)
next = next.tb_next
info['error_note'] = "Could not construct oldspace!\n" + s
# properties for the sidebar
prop = []
if WMFS._cuspidal == 1:
prop = [('Dimension newforms', [info['dimension_newspace']])]
prop.append(('Dimension oldforms', [info['dimension_oldspace']]))
else:
prop = [('Dimension modular forms', [info['dimension_mod_forms']])]
prop.append(('Dimension cusp forms', [info['dimension_cusp_forms']]))
prop.append(('Sturm bound', [WMFS.sturm_bound()]))
info['properties2'] = prop
## Make parent spaces of S_k(N,chi) for the sidebar
par_lbl = '\( S_{*} (\Gamma_0(' + str(level) + '),\cdot )\)'
par_url = '?level=' + str(level)
parents = [[par_lbl, par_url]]
par_lbl = '\( S_{k} (\Gamma_0(' + str(level) + '),\cdot )\)'
par_url = '?level=' + str(level) + '&weight=' + str(weight)
parents.append((par_lbl, par_url))
info['parents'] = parents
if 'character' in info:
info['character_order'] = WMFS.character_order()
info['character_conductor'] = WMFS.character_conductor()
friends = list()
lifts = list()
if(('label' not in info) and info['old_decomposition'] != 'n/a'):
O = WMFS.oldspace_decomposition()
try:
for (old_level, chi, mult, d) in O:
if chi != 0:
s = "\(S_{%s}(\Gamma_0(%s),\chi_{%s}) \) " % (weight, old_level, chi)
friends.append((
s, '?weight=' + str(weight) + '&level=' + str(old_level) + '&character=' + str(chi)))
else:
s = "\(S_{%s}(\Gamma_0(%s)) \) " % (weight, old_level)
friends.append(
(s, '?weight=' + str(weight) + '&level=' + str(old_level) + '&character=' + str(0)))
except:
pass
info['friends'] = friends
lifts.append(('Half-Integral Weight Forms', '/ModularForm/Mp2/Q'))
lifts.append(('Siegel Modular Forms', '/ModularForm/GSp4/Q'))
info['lifts'] = lifts
return info
def set_info_for_web_newform(level=None,
weight=None,
character=None,
label=None,
**kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(
level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'bprec', default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm_cached(level=level,
weight=weight,
character=character,
label=label)
emf_logger.critical("defined webnewform for rendering!")
# if info.has_key('download') and info.has_key('tempfile'):
# WNF._save_to_file(info['tempfile'])
# info['filename']=str(weight)+'-'+str(level)+'-'+str(character)+'-'+label+'.sobj'
# return info
except IndexError as e:
WNF = None
info['error'] = e.message
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight,
character=character)
bread = [(EMF_TOP, url1)]
bread.append(("of level %s" % level, url2))
bread.append(("weight %s" % weight, url3))
if int(character) == 0:
bread.append(("trivial character", url4))
else:
bread.append(("\( %s \)" % (WNF.character.latex_name), url4))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character)
friends.append(
('\( S_{%s}(%s, %s)\)' %
(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if WNF.coefficient_field_label(check=True):
friends.append(('Number field ' + WNF.coefficient_field_label(),
WNF.coefficient_field_url()))
friends.append(
('Number field ' + WNF.base_field_label(), WNF.base_field_url()))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)",
WNF.character.url()))
if WNF.dimension == 0:
info['error'] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
#info['name'] = name
info['title'] = 'Modular Form ' + WNF.hecke_orbit_label
if 'error' in info:
return info
# info['name']=WNF._name
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if WNF.coefficient_field.absolute_degree() == 1:
rdeg = 1
else:
rdeg = WNF.coefficient_field.relative_degree()
if cdeg == 1:
info['satake'] = WNF.satake
info['qexp'] = WNF.q_expansion_latex(prec=10, name='a')
info['qexp_display'] = url_for(".get_qexp_latex",
level=level,
weight=weight,
character=character,
label=label)
# info['qexp'] = WNF.q_expansion_latex(prec=prec)
#c_pol_st = str(WNF.absolute_polynomial)
#b_pol_st = str(WNF.polynomial(type='base_ring',format='str'))
#b_pol_ltx = str(WNF.polynomial(type='base_ring',format='latex'))
#print "c=",c_pol_ltx
#print "b=",b_pol_ltx
if cdeg > 1: ## Field is QQ
if bdeg > 1 and rdeg > 1:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = latex(p1)
lgc = p1.variables()[0]
c_pol_ltx = c_pol_ltx.replace(lgc, 'a')
z = p1.base_ring().gens()[0]
p2 = z.minpoly()
b_pol_ltx = latex(p2)
b_pol_ltx = b_pol_ltx.replace(latex(p2.variables()[0]), latex(z))
info['polynomial_st'] = 'where \({0}=0\) and \({1}=0\).'.format(
c_pol_ltx, b_pol_ltx)
else:
c_pol_ltx = latex(WNF.coefficient_field.relative_polynomial())
lgc = str(
latex(WNF.coefficient_field.relative_polynomial().variables()
[0]))
c_pol_ltx = c_pol_ltx.replace(lgc, 'a')
info['polynomial_st'] = 'where \({0}=0\)'.format(c_pol_ltx)
else:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg == 1:
info['is_rational'] = 1
else:
info['is_rational'] = 0
# info['q_exp_embeddings'] = WNF.print_q_expansion_embeddings()
# if(int(info['degree'])>1 and WNF.dimension()>1):
# s = 'One can embed it into \( \mathbb{C} \) as:'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# elif(int(info['degree'])>1):
# s = 'There are '+str(info['degree'])+' embeddings into \( \mathbb{C} \):'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# else:
# info['embeddings'] = ''
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings[
'values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = []
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'],
list) and len(info['twist_info']) > 0:
info['is_minimal'] = info['twist_info'][0]
if (info['twist_info'][0]):
s = '- Is minimal<br>'
else:
s = '- Is a twist of lower level<br>'
properties2 = [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 = [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm is None:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm is True:
s = '- Is a CM-form<br>'
else:
s = '- Is not a CM-form<br>'
properties2.append(('CM info', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev, dict) and len(alev.keys()) > 0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if (level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6', '')
if poly <> '':
d, monom, coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(d):
c = QQ(coeffs[i])
s = ""
if d > 1 and i > 0 and c > 0:
s = "+"
if c < 0:
s = "-"
if c.denominator() > 1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(
abs(c.numerator()), c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]
b = monom[i][1]
if a == 0 and b <> 0:
s += "E_6^{{ {0} }}".format(b)
elif b == 0 and a <> 0:
s += "E_4^{{ {0} }}".format(a)
else:
s += "E_4^{{ {0} }}E_6^{{ {1} }}".format(a, b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if (label_other != label):
s = 'Modular form '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(
character) + str(label_other)
else:
s = s + str(level) + '.' + str(weight) + str(label_other)
url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(
label)
else:
s = s + str(level) + '.' + str(weight) + str(label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label)
if WNF.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_degree):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight == 2 and WNF.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_cn()
return info
def set_info_for_modular_form_space(level=None, weight=None, character=None, label=None, **kwds):
r"""
Set information about a space of modular forms.
"""
info = dict()
emf_logger.debug("info={0}".format(info))
WMFS = None
if info.has_key('error'):
return info
if level <= 0:
info['error'] = "Got wrong level: %s " % level
return info
try:
WMFS = WebModFormSpace_cached(level = level, weight = weight, cuspidal=True, character = character, update_from_db=True)
WMFS.update_from_db() ## Need to call an extra time for some reason...
if not WMFS.has_updated():
stop = False
orbit = WMFS.character.character.galois_orbit()
while not stop:
if len(orbit) == 0:
stop = True
continue
c = orbit.pop()
if c.number() == WMFS.character.number:
continue
print c.number()
WMFS_rep = WebModFormSpace_cached(level = level, weight = weight, cuspidal=True, character = c.number(), update_from_db=True)
if WMFS_rep.has_updated_from_db():
stop = True
info['wmfs_rep_url'] = url_for('emf.render_elliptic_modular_forms', level=level, weight=weight, character = c.number())
info['wmfs_rep_number'] = c.number()
emf_logger.debug("Created WebModFormSpace %s"%WMFS)
if 'download' in info and 'tempfile' in info:
save(WNF,info['tempfile'])
info['filename'] = str(weight) + '-' + str(level) + '-' + str(character) + '-' + label + '.sobj'
return info
except ValueError as e:
emf_logger.debug(e)
emf_logger.debug(e.message)
#if isinstance(e,IndexError):
info['error'] = e.message
WMFS = None
if WMFS is None:
info['error'] = "We are sorry. The sought space can not be found in the database. "+"<br> Detailed information: {0}".format(info.get('error',''))
return info
else:
### Somehow the Hecke orbits are sometimes not in the space...
#if WMFS.dimension_new_cusp_forms()!=len(WMFS.hecke_orbits):
# ## Try to add them here...
# for d in range(len(WMFS.dimension_new_cusp_forms())):
# F =
# WMFS.hecke_orbits.append(F)
info['space'] = WMFS
# info['old_decomposition'] = WMFS.oldspace_decomposition()
info['oldspace_decomposition']=''
try:
emf_logger.debug("Oldspace = {0}".format(WMFS.oldspace_decomposition))
if WMFS.oldspace_decomposition != []:
emf_logger.debug("oldspace={0}".format(WMFS.oldspace_decomposition))
l = []
for t in WMFS.oldspace_decomposition:
emf_logger.debug("t={0}".format(t))
N,k,chi,mult,d = t
url = url_for('emf.render_elliptic_modular_forms', level=N, weight=k, character=chi)
if chi != 1:
sname = "S^{{ new }}_{{ {k} }}(\\Gamma_0({N}),\\chi_{{ {N} }}({chi},\\cdot))".format(k=k,N=N,chi=chi)
else:
sname = "S^{{ new }}_{{ {k} }}(\\Gamma_0({N}))".format(k=k,N=N)
l.append("\href{{ {url} }}{{ {sname} }}^{{\oplus {mult} }}".format(sname=sname,mult=mult,url=url))
if l != []:
s = "\\oplus ".join(l)
info['oldspace_decomposition']=' $ {0} $'.format(s)
except Exception as e:
emf_logger.critical("Oldspace decomposition failed. Error:{0}".format(e))
## For side-bar
lifts = list()
lifts.append(('Half-Integral Weight Forms', '/ModularForm/Mp2/Q'))
lifts.append(('Siegel Modular Forms', '/ModularForm/GSp4/Q'))
info['lifts'] = lifts
friends = list()
for label in WMFS.hecke_orbits:
f = WMFS.hecke_orbits[label]
# catch the url being None or set to '':
if hasattr(f.base_ring, "lmfdb_url") and f.base_ring.lmfdb_url:
friends.append(('Number field ' + f.base_ring.lmfdb_pretty, f.base_ring.lmfdb_url))
if hasattr(f.coefficient_field, "lmfdb_url") and f.coefficient_field.lmfdb_url:
friends.append(('Number field ' + f.coefficient_field.lmfdb_pretty, f.coefficient_field.lmfdb_url))
friends.append(("Dirichlet character \(" + WMFS.character.latex_name + "\)", WMFS.character.url()))
friends = uniq(friends)
info['friends'] = friends
return info
def set_table_browsing(self,
skip=[0, 0],
limit=[(2, 16), (1, 50)],
keys=['Weight', 'Level'],
character=0,
dimension_table=None,
dimension_fun=dimension_new_cusp_forms,
title='Dimension of newforms',
check_db=True):
r"""
Table of Holomorphic modular forms spaces.
Skip tells you how many chunks of data you want to skip (from the geginning) and limit tells you how large each chunk is.
INPUT:
- dimension_fun should be a function which gives you the desired dimensions, as functions of level N and weight k
- character = 0 for trivial character and 1 for Kronecker symbol.
set to 'all' for all characters.
- check_db=True means, that we will only link to spaces which are in the database
"""
self._keys = keys
self._skip = skip
self._limit = limit
self._metadata = []
self._title = ''
self._cols = []
self.table = {}
self._character = character
emf_logger.debug("skip= {0}".format(self._skip))
emf_logger.debug("limit= {0}".format(self._limit))
il = self._keys.index('Level')
iwt = self._keys.index('Weight')
level_len = self._limit[il][1] - self._limit[il][0] + 1
level_ll = self._skip[il] * level_len + self._limit[il][0]
level_ul = self._skip[il] * level_len + self._limit[il][1]
wt_len = self._limit[iwt][1] - self._limit[iwt][0] + 1
wt_ll = self._skip[iwt] * wt_len + self._limit[iwt][0]
wt_ul = self._skip[iwt] * wt_len + self._limit[iwt][1]
if level_ll < 1:
level_l = 1
self._table = {}
self._table['rows'] = []
self._table['col_heads'] = [] # range(wt_ll,wt_ul+1)
self._table['row_heads'] = [] # range(level_ll,level_ul+1)
emf_logger.debug("wt_range: {0} -- {1}".format(wt_ll, wt_ul))
emf_logger.debug("level_range: {0} -- {1}".format(level_ll, level_ul))
emf_logger.debug("character: {0}".format(character))
self._table['characters'] = dict()
if dimension_table is not None:
dimension_fun = dimension_table.dimension
is_data_in_db = dimension_table.is_in_db
factors = connect_db()['Newform_factors.files']
list_of_data = factors.distinct('hecke_orbit_label')
#else:
#def is_data_in_db(N, k, character):
# n = self._files.find({'N':int(N),'k':int(k),'chi':int(character)}).count()
# emf_logger.debug("is_Data_in: N,k,character: {0} no. recs: {1} in {2}".format((N,k,character),n,self._files))
# return n>0
# fixed level
if level_ll == level_ul:
N = level_ll
# specific character =0,1
if character == 0 or character == 1:
self._table['rowhead'] = 'Weight'
if character == 0:
cchi = 1 #xc = DirichletGroup_conrey(N)[1]
else:
D = DirichletGroup_conrey(N)
for xc in D:
x = xc.sage_character()
if x == kronecker_character_upside_down(N):
cchi = xc.number()
break
row = dict()
row['head'] = "\(\chi_{" + str(N) + "}(" + str(
cchi) + ",\cdot) \)"
row['url'] = url_for('characters.render_Dirichletwebpage',
modulus=N,
number=cchi)
row['cells'] = list()
for k in range(wt_ll, wt_ul + 1):
if character == 0 and is_odd(k):
continue
try:
if character == 0:
d = dimension_fun(N, k)
elif character == 1:
d = dimension_fun(x, k)
except Exception as ex:
emf_logger.critical(
"Exception: {0}. \n Could not compute the dimension with function {0}"
.format(ex, dimension_fun))
if (not check_db) or "{0}.{1}.{2}a".format(
N, k, cchi
) in list_of_data: #is_data_in_db(N, k, character):
url = url_for('emf.render_elliptic_modular_forms',
level=N,
weight=k,
character=character)
else:
url = ''
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
row['cells'].append({'N': N, 'k': k, 'url': url, 'dim': d})
self._table['rows'].append(row)
else:
D = DirichletGroup(N)
G = D.galois_orbits()
Greps = [X[0] for X in G]
Dc = DirichletGroup_conrey(N)
Gcreps = dict()
# A security check, if we have at least weight 2 and trivial character,
# otherwise don't show anything
#if check_db and not is_data_in_db(N, 2, 0):
# emf_logger.debug("No data for level {0} and weight 2, trivial character".format(N)#)
#self._table = None
# return None
Gc = dict()
for xi, g in enumerate(G):
Gc[xi] = list()
self._table['maxGalCount'] = 0
for xc in Dc:
x = xc.sage_character()
xi = G.index(x.galois_orbit())
# emf_logger.debug('Dirichlet Character Conrey {0} = sage_char {1}, has
# Galois orbit nr. {2}'.format(xc,x,xi))
Gc[xi].append(xc)
if x == Greps[xi]:
Gcreps[xi] = xc
emf_logger.debug('Gc={0}'.format(Gc))
for xi in Gc:
g = Gc[xi]
if len(g) > self._table['maxGalCount']:
self._table['maxGalCount'] = len(g)
emf_logger.debug('xi,g={0},{1}'.format(xi, g))
x = Greps[xi]
xc = Gcreps[xi]
cchi = xc.number()
row = dict()
row['head'] = "\(\chi_{" + str(N) + "}(" + str(
cchi) + ",\cdot) \)"
row['url'] = url_for('characters.render_Dirichletwebpage',
modulus=N,
number=cchi)
row['galois_orbit'] = [{
'chi':
str(xc.number()),
'url':
url_for('characters.render_Dirichletwebpage',
modulus=N,
number=cchi)
} for xc in g]
row['cells'] = []
for k in range(wt_ll, wt_ul + 1):
if not k in self._table['col_heads']:
# emf_logger.debug("Adding to col_heads:{0}s".format(k))
self._table['col_heads'].append(k)
try:
d = dimension_fun(x, k)
except Exception as ex:
emf_logger.critical(
"Exception: {0} \n Could not compute the dimension with function {1}"
.format(ex, dimension_fun))
if (not check_db) or "{0}.{1}.{2}a".format(
N, k, cchi
) in list_of_data: #is_data_in_db(N, k, xi):
url = url_for('emf.render_elliptic_modular_forms',
level=N,
weight=k,
character=xi)
else:
url = ''
row['cells'].append({
'N': N,
'k': k,
'chi': xi,
'url': url,
'dim': d
})
self._table['rows'].append(row)
else:
for k in range(wt_ll, wt_ul + 1):
if character == 0 and is_odd(k):
continue
row = []
for N in range(level_ll, level_ul + 1):
if not N in self._table['col_heads']:
self._table['col_heads'].append(N)
try:
if character == 0:
d = dimension_fun(N, k)
elif character == 1:
x = kronecker_character_upside_down(N)
d = dimension_fun(x, k)
else:
d = dimension_fun(N, k)
except Exception as ex:
emf_logger.critical(
"Exception: {0}. \n Could not compute the dimension with function {0}"
.format(ex, dimension_fun))
# emf_logger.debug("N,k,char,dim: {0},{1},{2},{3}".format(N,k,character,d))
if character == 0 or character == 1:
if (not check_db) or "{0}.{1}.{2}a".format(
N, k, 1
) in list_of_data: #is_data_in_db(N, k, character):
url = url_for('emf.render_elliptic_modular_forms',
level=N,
weight=k,
character=character)
else:
url = ''
else:
t1 = "{0}.{1}.{2}a".format(N, k, 1)
t2 = "{0}.{1}.{2}a".format(N, k, 2)
if (
not check_db
) or t1 in list_of_data or t2 in list_of_data: # is_data_in_db(N, k, character):
url = url_for('emf.render_elliptic_modular_forms',
level=N,
weight=k)
else:
url = ''
if not k in self._table['row_heads']:
self._table['row_heads'].append(k)
row.append({'N': N, 'k': k, 'url': url, 'dim': d})
emf_logger.debug("row:{0}".format(row))
self._table['rows'].append(row)
def update_from_db(self, ignore_non_existent = True, \
add_to_fs_query=None, add_to_db_query=None):
r"""
Updates the properties of ```self``` from the database using params and dbkey.
"""
self._has_updated_from_db = False
self._has_updated_from_fs = False
if add_to_db_query is None:
add_to_db_query = self._add_to_db_query
elif self._add_to_db_query is not None:
q = add_to_db_query
add_to_db_query = copy(self._add_to_db_query)
add_to_db_query.update(q)
if add_to_fs_query is None:
add_to_fs_query = self._add_to_fs_query
elif self._add_to_fs_query is not None:
q = add_to_fs_query
add_to_fs_query = copy(self._add_to_fs_query)
add_to_fs_query.update(q)
#emf_logger.debug("add_to_fs_query: {0}".format(add_to_fs_query))
#emf_logger.debug("self._add_to_fs_query: {0}".format(self._add_to_fs_query))
emf_logger.debug("db_properties: {0}".format(self._db_properties))
succ_db = False
succ_fs = False
if self._use_separate_db or not self._use_gridfs:
coll = self._collection
key = self.key_dict()
if add_to_db_query is not None:
key.update(add_to_db_query)
emf_logger.debug("key: {0} for {1}".format(key,
self._collection_name))
if coll.find(key).count() > 0:
props_to_fetch = {} #p.name:True for p in self._key}
for p in self._db_properties:
if p.include_in_update and (
not p.name in self._fs_properties
or p._extend_fs_with_db):
props_to_fetch[p.name] = True
p.has_been_set(False)
# props_to_fetch = {p.name:True for p in self._db_properties
# if (p.include_in_update and not p.name in self._fs_properties)
# or p.name in self._key}
emf_logger.debug("props_to_fetch: {0}".format(props_to_fetch))
rec = coll.find_one(key, projection=props_to_fetch)
for pn in props_to_fetch:
p = self._properties[pn]
if rec.has_key(pn):
try:
p.set_from_db(rec[pn])
if not p.name in self._fs_properties:
p.has_been_set(True)
except NotImplementedError:
continue
succ_db = True
else:
emf_logger.critical(
"record with key:{0} was not found!".format(key))
if not ignore_non_existent:
raise IndexError("DB record does not exist")
succ_db = False
if self._use_gridfs:
fs = self._files
file_key = self.file_key_dict()
if add_to_fs_query is not None:
file_key.update(add_to_fs_query)
emf_logger.debug("add_to_fs_query: {0}".format(add_to_fs_query))
emf_logger.debug("file_key: {0} fs={1}".format(
file_key, self._file_collection))
if fs.exists(file_key):
coll = self._file_collection
r = coll.find_one(file_key)
fid = r['_id']
#emf_logger.debug("col={0}".format(coll))
#emf_logger.debug("rec={0}".format(coll.find_one(file_key)))
try:
d = loads(fs.get(fid).read())
except ValueError as e:
raise ValueError(
"Wrong format in database! : {0} coll: {1} rec:{2}".
format(e, coll, r))
#emf_logger.debug("type(d)={0}".format(type(d)))
#emf_logger.debug("d.keys()={0}".format(d.keys()))
for p in self._fs_properties:
#emf_logger.debug("p={0}, update:{1}".format(p,p.include_in_update))
#emf_logger.debug("d[{0}]={1}".format(p.name,type(d.get(p.name))))
if p.include_in_update and d.has_key(p.name):
emf_logger.debug("d[{0}]={1}".format(
p.name, type(d.get(p.name))))
p.has_been_set(False)
p.set_from_fs(d[p.name])
succ_fs = True
else:
if not ignore_non_existent:
raise IndexError("File does not exist")
succ_fs = False
emf_logger.debug("loaded from fs")
if succ_db: self._has_updated_from_db = True
if succ_fs: self._has_updated_from_fs = True
def set_table_browsing(self, skip=[0, 0], limit=[(2, 16), (1, 50)], keys=['Weight', 'Level'], character=0, dimension_table=None, dimension_fun=dimension_new_cusp_forms, title='Dimension of newforms', check_db=True):
r"""
Table of Holomorphic modular forms spaces.
Skip tells you how many chunks of data you want to skip (from the geginning) and limit tells you how large each chunk is.
INPUT:
- dimension_fun should be a function which gives you the desired dimensions, as functions of level N and weight k
- character = 0 for trivial character and 1 for Kronecker symbol.
set to 'all' for all characters.
- check_db=True means, that we will only link to spaces which are in the database
"""
self._keys = keys
self._skip = skip
self._limit = limit
self._metadata = []
self._title = ''
self._cols = []
self.table = {}
self._character = character
emf_logger.debug("skip= {0}".format(self._skip))
emf_logger.debug("limit= {0}".format(self._limit))
il = self._keys.index('Level')
iwt = self._keys.index('Weight')
level_len = self._limit[il][1] - self._limit[il][0] + 1
level_ll = self._skip[il] * level_len + self._limit[il][0]
level_ul = self._skip[il] * level_len + self._limit[il][1]
wt_len = self._limit[iwt][1] - self._limit[iwt][0] + 1
wt_ll = self._skip[iwt] * wt_len + self._limit[iwt][0]
wt_ul = self._skip[iwt] * wt_len + self._limit[iwt][1]
if level_ll < 1:
level_l = 1
self._table = {}
self._table['rows'] = []
self._table['col_heads'] = [] # range(wt_ll,wt_ul+1)
self._table['row_heads'] = [] # range(level_ll,level_ul+1)
emf_logger.debug("wt_range: {0} -- {1}".format(wt_ll, wt_ul))
emf_logger.debug("level_range: {0} -- {1}".format(level_ll, level_ul))
emf_logger.debug("character: {0}".format(character))
self._table['characters'] = dict()
if dimension_table is not None:
dimension_fun = dimension_table.dimension
is_data_in_db = dimension_table.is_in_db
else:
def is_data_in_db(N, k, character):
return False
# fixed level
if level_ll == level_ul:
N = level_ll
# specific character =0,1
if character == 0 or character == 1:
self._table['rowhead'] = 'Weight'
if character == 0:
xc = DirichletGroup_conrey(N)[1]
else:
D = DirichletGroup_conrey(N)
for xc in D:
if xc.sage_character() == kronecker_character_upside_down(N):
break
x = xc.sage_character()
row = dict()
row['head'] = "\(\chi_{" + str(N) + "}(" + str(xc.number()) + ",\cdot) \)"
row['url'] = url_character(type='Dirichlet', modulus=N, number=xc.number())
row['cells'] = list()
for k in range(wt_ll, wt_ul + 1):
if character == 0 and is_odd(k):
continue
try:
if character == 0:
d = dimension_fun(N, k)
elif character == 1:
d = dimension_fun(x, k)
except Exception as ex:
emf_logger.critical("Exception: {0}. \n Could not compute the dimension with function {0}".format(ex, dimension_fun))
if (not check_db) or is_data_in_db(N, k, character):
url = url_for(
'emf.render_elliptic_modular_forms', level=N, weight=k, character=character)
else:
url = ''
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
row['cells'].append({'N': N, 'k': k, 'url': url, 'dim': d})
self._table['rows'].append(row)
else:
D = DirichletGroup(N)
G = D.galois_orbits()
Greps = [X[0] for X in G]
Dc = DirichletGroup_conrey(N)
Gcreps = dict()
# A security check, if we have at least weight 2 and trivial character,
# otherwise don't show anything
if check_db and not is_data_in_db(N, 2, 0):
emf_logger.debug("No data for level {0} and weight 2, trivial character".format(N))
self._table = None
return None
Gc = dict()
for xi, g in enumerate(G):
Gc[xi] = list()
self._table['maxGalCount'] = 0
for xc in Dc:
x = xc.sage_character()
xi = G.index(x.galois_orbit())
# emf_logger.debug('Dirichlet Character Conrey {0} = sage_char {1}, has
# Galois orbit nr. {2}'.format(xc,x,xi))
Gc[xi].append(xc)
if x == Greps[xi]:
Gcreps[xi] = xc
emf_logger.debug('Gc={0}'.format(Gc))
for xi in Gc:
g = Gc[xi]
if len(g) > self._table['maxGalCount']:
self._table['maxGalCount'] = len(g)
emf_logger.debug('xi,g={0},{1}'.format(xi, g))
x = Greps[xi]
xc = Gcreps[xi]
row = dict()
row['head'] = "\(\chi_{" + str(N) + "}(" + str(xc.number()) + ",\cdot) \)"
row['url'] = url_character(type='Dirichlet', modulus=N, number=xc.number())
row['galois_orbit'] = [
{'chi': str(xc.number()),
'url': url_character(type='Dirichlet', modulus=N, number=xc.number()) }
for xc in g]
row['cells'] = []
for k in range(wt_ll, wt_ul + 1):
if not k in self._table['col_heads']:
# emf_logger.debug("Adding to col_heads:{0}s".format(k))
self._table['col_heads'].append(k)
try:
d = dimension_fun(x, k)
except Exception as ex:
emf_logger.critical("Exception: {0} \n Could not compute the dimension with function {1}".format(ex, dimension_fun))
if (not check_db) or is_data_in_db(N, k, xi):
url = url_for(
'emf.render_elliptic_modular_forms', level=N, weight=k, character=xi)
else:
url = ''
row['cells'].append({'N': N, 'k': k, 'chi': xi, 'url': url, 'dim': d})
self._table['rows'].append(row)
else:
for k in range(wt_ll, wt_ul + 1):
if character == 0 and is_odd(k):
continue
row = []
for N in range(level_ll, level_ul + 1):
if not N in self._table['col_heads']:
self._table['col_heads'].append(N)
try:
if character == 0:
d = dimension_fun(N, k)
elif character == 1:
x = kronecker_character_upside_down(N)
d = dimension_fun(x, k)
else:
d = dimension_fun(N, k)
except Exception as ex:
emf_logger.critical("Exception: {0}. \n Could not compute the dimension with function {0}".format(ex, dimension_fun))
# emf_logger.debug("N,k,char,dim: {0},{1},{2},{3}".format(N,k,character,d))
if character == 0 or character == 1:
if (not check_db) or is_data_in_db(N, k, character):
url = url_for(
'emf.render_elliptic_modular_forms', level=N, weight=k, character=character)
else:
url = ''
else:
url = url_for('emf.render_elliptic_modular_forms', level=N, weight=k)
if not k in self._table['row_heads']:
self._table['row_heads'].append(k)
row.append({'N': N, 'k': k, 'url': url, 'dim': d})
self._table['rows'].append(row)
def set_info_for_gamma1(level,weight,weight2=None):
dimension_table_name = WebModFormSpace._dimension_table_name
if weight != None and weight2>weight:
w1 = weight; w2 = weight2
else:
w1 = weight; w2 = weight
table = {'galois_orbit':{},'galois_orbits_reps':{},'cells':{}}
table['weights']=range(w1,w2+1)
emf_logger.debug("dimension table name={0}".format(dimension_table_name))
db_dim = getDBConnection()['modularforms2'][dimension_table_name]
s = {'level':int(level),'weight':{"$lt":int(w2+1),"$gt":int(w1-1)},'cchi':{"$exists":True}}
q = db_dim.find(s).sort([('cchi',int(1)),('weight',int(1))])
if q.count() == 0:
emf_logger.debug("No spaces in the database!")
flash('The database does not currently contain any spaces matching these parameters. Please try again!')
return None #'error':'The database does not currently contain any spaces matching these parameters!'}
else:
table['maxGalCount']=1
for r in q:
xi = r['cchi']
orbit = r['character_orbit']
k = r['weight']
## This is probably still quicker if it is in the database
parity = r.get('character_parity','n/a')
if parity == 'n/a':
chi = ConreyCharacter(level,xi)
if chi.is_odd():
parity = -1
elif chi.is_even():
parity = 1
else:
emf_logger.critical("Could not determine the parity of ConreyCharacter({0},{1})".format(xi,level))
trivial_trivially = ""
if parity != 'n/a':
if k % 2 == (1 + parity)/2: # is space empty because of parity?
trivial_trivially = "yes"
else:
trivial_trivially = ""
if parity == 1:
parity = 'even'
elif parity == -1:
parity = 'odd'
d = r.get('d_newf',"n/a")
indb = r.get('in_wdb',0)
if d == 0:
indb = 1
if indb:
url = url_for('emf.render_elliptic_modular_forms', level=level, weight=k, character=xi)
else:
url = ''
if not table['galois_orbits_reps'].has_key(xi):
table['galois_orbits_reps'][xi]={
'head' : "\(\chi_{{{0}}}({1},\cdot) \)".format(level,xi), # yes, {{{ is required
'chi': "{0}".format(xi),
'url': url_for('characters.render_Dirichletwebpage', modulus=level, number=xi),
'parity':parity}
table['galois_orbit'][xi]= [
{
#'head' : "\(\chi_{{{0}}}({1},\cdot) \)".format(level,xci), # yes, {{{ is required
## 'head' : "\(S_{{{0}}}({1},\chi({2}, \cdot) ) \)".format(weight,level,xci), # yes, {{{ is required
## 'head' : "\(S_{{{0}}}(\chi({1}, \cdot) ) \)".format(weight,xci), # yes, {{{ is required
'head' : r"\(S_{{{0}}}(\chi_{{{1}}}({2}, \cdot)) \)".format(weight,level,xci), # yes, {{{ is required
# 'head' : "\({0}\)".format(xci),
'chi': "{0}".format(xci),
# 'url': url_for('characters.render_Dirichletwebpage', modulus=level, number=xci)
'url': url_for('emf.render_elliptic_modular_forms', level=level, weight=k, character=xci) if indb else ''
}
for xci in orbit]
if len(orbit)>table['maxGalCount']:
table['maxGalCount']=len(orbit)
table['cells'][xi]={}
table['cells'][xi][k] ={'N': level, 'k': k, 'chi': xi, 'url': url, 'dim': d, 'trivial_trivially': trivial_trivially,}
table['galois_orbits_reps_numbers']=table['galois_orbits_reps'].keys()
table['galois_orbits_reps_numbers'].sort()
#emf_logger.debug("Table:{0}".format(table))
return table
def set_info_for_gamma1(level, weight, weight2=None):
from lmfdb.modular_forms.elliptic_modular_forms.backend.emf_utils import (
dimension_from_db,
dirichlet_character_conrey_galois_orbits_reps,
conrey_character_from_number,
)
from sage.all import DirichletGroup, dimension_new_cusp_forms
from dirichlet_conrey import DirichletGroup_conrey
from lmfdb.modular_forms.elliptic_modular_forms import WebModFormSpace
dimension_table_name = WebModFormSpace._dimension_table_name
dim_table = dimension_from_db(level, weight, chi="all", group="gamma1")
if weight != None and weight2 > weight:
w1 = weight
w2 = weight2
else:
w1 = weight
w2 = weight
table = {"galois_orbit": {}, "galois_orbits_reps": {}, "cells": {}}
table["weights"] = range(w1, w2 + 1)
max_gal_count = 0
from lmfdb.base import getDBConnection
emf_logger.debug("dimension table name={0}".format(dimension_table_name))
db_dim = getDBConnection()["modularforms2"][dimension_table_name]
s = {"level": int(level), "weight": {"$lt": int(w2 + 1), "$gt": int(w1 - 1)}, "cchi": {"$exists": True}}
q = db_dim.find(s).sort([("cchi", int(1)), ("weight", int(1))])
if q.count() == 0:
emf_logger.debug("No spaces in the database!")
flash("The database does not currently contain any spaces matching these parameters. Please try again!")
return None #'error':'The database does not currently contain any spaces matching these parameters!'}
else:
table["maxGalCount"] = 1
for r in q:
xi = r["cchi"]
orbit = r["character_orbit"]
k = r["weight"]
## This is probably still quicker if it is in the database
parity = r.get("character_parity", "n/a")
if parity == "n/a":
chi = ConreyCharacter(level, xi)
if chi.is_odd():
parity = -1
elif chi.is_even():
parity = 1
else:
emf_logger.critical("Could not determine the parity of ConreyCharacter({0},{1})".format(xi, level))
trivial_trivially = ""
if parity != "n/a":
if k % 2 == (1 + parity) / 2: # is space empty because of parity?
trivial_trivially = "yes"
else:
trivial_trivially = ""
if parity == 1:
parity = "even"
elif parity == -1:
parity = "odd"
d = r.get("d_newf", "n/a")
indb = r.get("in_wdb", 0)
if d == 0:
indb = 1
if indb:
url = url_for("emf.render_elliptic_modular_forms", level=level, weight=k, character=xi)
else:
url = ""
if not table["galois_orbits_reps"].has_key(xi):
table["galois_orbits_reps"][xi] = {
"head": "\(\chi_{{{0}}}({1},\cdot) \)".format(level, xi), # yes, {{{ is required
"chi": "{0}".format(xi),
"url": url_for("characters.render_Dirichletwebpage", modulus=level, number=xi),
"parity": parity,
}
table["galois_orbit"][xi] = [
{
#'head' : "\(\chi_{{{0}}}({1},\cdot) \)".format(level,xci), # yes, {{{ is required
## 'head' : "\(S_{{{0}}}({1},\chi({2}, \cdot) ) \)".format(weight,level,xci), # yes, {{{ is required
## 'head' : "\(S_{{{0}}}(\chi({1}, \cdot) ) \)".format(weight,xci), # yes, {{{ is required
"head": r"\(S_{{{0}}}(\chi_{{{1}}}({2}, \cdot)) \)".format(
weight, level, xci
), # yes, {{{ is required
# 'head' : "\({0}\)".format(xci),
"chi": "{0}".format(xci),
# 'url': url_for('characters.render_Dirichletwebpage', modulus=level, number=xci)
"url": url_for("emf.render_elliptic_modular_forms", level=level, weight=k, character=xci)
if indb
else "",
}
for xci in orbit
]
if len(orbit) > table["maxGalCount"]:
table["maxGalCount"] = len(orbit)
table["cells"][xi] = {}
table["cells"][xi][k] = {
"N": level,
"k": k,
"chi": xi,
"url": url,
"dim": d,
"trivial_trivially": trivial_trivially,
}
table["galois_orbits_reps_numbers"] = table["galois_orbits_reps"].keys()
table["galois_orbits_reps_numbers"].sort()
# emf_logger.debug("Table:{0}".format(table))
return table
def update_from_db(self, ignore_non_existent = True, \
add_to_fs_query=None, add_to_db_query=None):
r"""
Updates the properties of ```self``` from the database using params and dbkey.
"""
self._has_updated_from_db = False
self._has_updated_from_fs = False
if add_to_db_query is None:
add_to_db_query = self._add_to_db_query
elif self._add_to_db_query is not None:
q=add_to_db_query
add_to_db_query = copy(self._add_to_db_query)
add_to_db_query.update(q)
if add_to_fs_query is None:
add_to_fs_query = self._add_to_fs_query
elif self._add_to_fs_query is not None:
q=add_to_fs_query
add_to_fs_query = copy(self._add_to_fs_query)
add_to_fs_query.update(q)
#emf_logger.debug("add_to_fs_query: {0}".format(add_to_fs_query))
#emf_logger.debug("self._add_to_fs_query: {0}".format(self._add_to_fs_query))
emf_logger.debug("db_properties: {0}".format(self._db_properties))
succ_db = False
succ_fs = False
if self._use_separate_db or not self._use_gridfs:
coll = self._collection
key = self.key_dict()
if add_to_db_query is not None:
key.update(add_to_db_query)
emf_logger.debug("key: {0} for {1}".format(key,self._collection_name))
if coll.find(key).count()>0:
props_to_fetch = { } #p.name:True for p in self._key}
for p in self._db_properties:
if p.include_in_update and (not p.name in self._fs_properties or p._extend_fs_with_db):
props_to_fetch[p.name] = True
p.has_been_set(False)
# props_to_fetch = {p.name:True for p in self._db_properties
# if (p.include_in_update and not p.name in self._fs_properties)
# or p.name in self._key}
emf_logger.debug("props_to_fetch: {0}".format(props_to_fetch))
rec = coll.find_one(key, projection = props_to_fetch)
for pn in props_to_fetch:
p = self._properties[pn]
if rec.has_key(pn):
try:
p.set_from_db(rec[pn])
if not p.name in self._fs_properties:
p.has_been_set(True)
except NotImplementedError:
continue
succ_db = True
else:
emf_logger.critical("record with key:{0} was not found!".format(key))
if not ignore_non_existent:
raise IndexError("DB record does not exist")
succ_db = False
if self._use_gridfs:
fs = self._files
file_key = self.file_key_dict()
if add_to_fs_query is not None:
file_key.update(add_to_fs_query)
emf_logger.debug("add_to_fs_query: {0}".format(add_to_fs_query))
emf_logger.debug("file_key: {0}".format(file_key))
if fs.exists(file_key):
coll = self._file_collection
fid = coll.find_one(file_key)['_id']
#emf_logger.debug("col={0}".format(coll))
#emf_logger.debug("rec={0}".format(coll.find_one(file_key)))
try:
d = loads(fs.get(fid).read())
except ValueError as e:
raise ValueError("Wrong format in database! : {0}".format(e))
#emf_logger.debug("type(d)={0}".format(type(d)))
#emf_logger.debug("d.keys()={0}".format(d.keys()))
for p in self._fs_properties:
#emf_logger.debug("p={0}, update:{1}".format(p,p.include_in_update))
#emf_logger.debug("d[{0}]={1}".format(p.name,type(d.get(p.name))))
if p.include_in_update and d.has_key(p.name):
p.has_been_set(False)
p.set_from_fs(d[p.name])
succ_fs = True
else:
if not ignore_non_existent:
raise IndexError("File does not exist")
succ_fs = False
if succ_db: self._has_updated_from_db = True
if succ_fs: self._has_updated_from_fs = True
def set_info_for_web_newform(level=None,
weight=None,
character=None,
label=None,
**kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(
level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'bprec', default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm_cached(level=level,
weight=weight,
character=character,
label=label)
if not WNF.has_updated():
raise IndexError(
"Unfortunately, we do not have this newform in the database.")
info['character_order'] = WNF.character.order
info['code'] = WNF.code
emf_logger.debug("defined webnewform for rendering!")
except IndexError as e:
info['error'] = e.message
url0 = url_for("mf.modular_form_main_page")
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight,
character=character)
bread = [(MF_TOP, url0), (EMF_TOP, url1)]
bread.append(("Level %s" % level, url2))
bread.append(("Weight %s" % weight, url3))
bread.append(("Character \( %s \)" % (WNF.character.latex_name), url4))
bread.append(
("Newform %d.%d.%d.%s" % (level, weight, int(character), label), ''))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character)
friends.append(
('\( S_{%s}(%s, %s)\)' %
(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if hasattr(WNF.base_ring, "lmfdb_url") and WNF.base_ring.lmfdb_url:
friends.append(('Number field ' + WNF.base_ring.lmfdb_pretty,
WNF.base_ring.lmfdb_url))
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_label:
friends.append(('Number field ' + WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_url))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)",
WNF.character.url()))
if WNF.dimension == 0 and not info.has_key('error'):
info['error'] = "This space is empty!"
info['title'] = 'Newform ' + WNF.hecke_orbit_label
info['learnmore'] = [('History of modular forms',
url_for('.holomorphic_mf_history'))]
if 'error' in info:
return info
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
## Example to illustrate the different cases
## base = CyclotomicField(n) -- of degree phi(n)
## coefficient_field = NumberField( p(x)) for some p in base['x'] of degree m
## we would then have cdeg = m*phi(n) and bdeg = phi(n)
## and rdeg = m
## Unfortunately, for e.g. base = coefficient_field = CyclotomicField(6)
## we get coefficient_field.relative_degree() == 2 although it should be 1
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if cdeg == 1:
rdeg = 1
else:
## just setting rdeg = WNF.coefficient_field.relative_degree() does not give correct result...
##
rdeg = QQ(cdeg) / QQ(bdeg)
cf_is_QQ = (cdeg == 1)
br_is_QQ = (bdeg == 1)
if cf_is_QQ:
info['satake'] = WNF.satake
if WNF.complexity_of_first_nonvanishing_coefficients(
) > default_max_height:
info['qexp'] = ""
info['qexp_display'] = ''
info['hide_qexp'] = True
n, c = WNF.first_nonvanishing_coefficient()
info['trace_nv'] = latex(WNF.first_nonvanishing_coefficient_trace())
info['norm_nv'] = '\\approx ' + latex(
WNF.first_nonvanishing_coefficient_norm().n())
info['index_nv'] = n
else:
if WNF.prec < prec:
#get WNF record at larger prec
WNF.prec = prec
WNF.update_from_db()
info['qexp'] = WNF.q_expansion_latex(prec=10, name='\\alpha ')
info['qexp_display'] = url_for(".get_qexp_latex",
level=level,
weight=weight,
character=character,
label=label)
info["hide_qexp"] = False
info['max_cn_qexp'] = WNF.q_expansion.prec()
## All combinations should be tested...
## 13/4/4/a -> base ring = coefficient_field = QQ(zeta_6)
## 13/3/8/a -> base_ring = QQ(zeta_4), coefficient_field has poly x^2+(2\zeta_4+2x-3\zeta_$ over base_ring
## 13/4/3/a -> base_ring = coefficient_field = QQ(zeta_3)
## 13/4/1/a -> all rational
## 13/6/1/a/ -> base_ring = QQ, coefficient_field = Q(sqrt(17))
## These are variables which needs to be set properly below
info['polvars'] = {'base_ring': 'x', 'coefficient_field': '\\alpha'}
if not cf_is_QQ:
if rdeg > 1: # not WNF.coefficient_field == WNF.base_ring:
## Here WNF.base_ring should be some cyclotomic field and we have an extension over this.
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1,
'\\alpha') # make the variable \alpha
c_pol_ltx_x = web_latex_poly(p1, 'x')
zeta = p1.base_ring().gens()[0]
# p2 = zeta.minpoly() #this is not used anymore
# b_pol_ltx = web_latex_poly(p2, latex(zeta)) #this is not used anymore
z1 = zeta.multiplicative_order()
info['coeff_field'] = [
WNF.coefficient_field.absolute_polynomial_latex('x'),
c_pol_ltx_x, z1
]
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url,
WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_label
]
if z1 == 4:
info[
'polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).</div><br/>'.format(
c_pol_ltx)
info['polvars']['base_ring'] = 'i'
elif z1 <= 2:
info[
'polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(
c_pol_ltx)
else:
info[
'polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\) ' % (
c_pol_ltx, z1, z1)
info['polvars']['base_ring'] = '\zeta_{{ {0} }}'.format(z1)
if z1 == 3:
info[
'polynomial_st'] += 'is a primitive cube root of unity.'
else:
info[
'polynomial_st'] += 'is a primitive {0}-th root of unity.'.format(
z1)
elif not br_is_QQ:
## Now we have base and coefficient field being equal, meaning that since the coefficient field is not QQ it is some cyclotomic field
## generated by some \zeta_n
p1 = WNF.coefficient_field.absolute_polynomial()
z1 = WNF.coefficient_field.gens()[0].multiplicative_order()
c_pol_ltx = web_latex_poly(p1, '\\zeta_{{{0}}}'.format(z1))
c_pol_ltx_x = web_latex_poly(p1, 'x')
info['coeff_field'] = [
WNF.coefficient_field.absolute_polynomial_latex('x'),
c_pol_ltx_x
]
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url,
WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_label
]
if z1 == 4:
info[
'polynomial_st'] = '<div class="where">where \(\zeta_4=e^{{\\frac{{\\pi i}}{{ 2 }} }}=i \).</div>'.format(
c_pol_ltx)
info['polvars']['coefficient_field'] = 'i'
elif z1 <= 2:
info['polynomial_st'] = ''
else:
info[
'polynomial_st'] = '<div class="where">where \(\zeta_{{{0}}}=e^{{\\frac{{2\\pi i}}{{ {0} }} }}\) '.format(
z1)
info['polvars']['coefficient_field'] = '\zeta_{{{0}}}'.format(
z1)
if z1 == 3:
info[
'polynomial_st'] += 'is a primitive cube root of unity.</div>'
else:
info[
'polynomial_st'] += 'is a primitive {0}-th root of unity.</div>'.format(
z1)
else:
info['polynomial_st'] = ''
if info["hide_qexp"]:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg == 1:
info['is_rational'] = 1
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty
]
else:
info['is_rational'] = 0
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings[
'values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = [('Level', str(level)), ('Weight', str(weight)),
('Character', '$' + WNF.character.latex_name + '$'),
('Label', WNF.hecke_orbit_label),
('Dimension of Galois orbit', str(WNF.dimension))]
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'],
list) and len(info['twist_info']) > 0:
info['is_minimal'] = info['twist_info'][0]
if (info['twist_info'][0]):
s = 'Is minimal<br>'
else:
s = 'Is a twist of lower level<br>'
properties2 += [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 += [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm == 1:
info['cm_field'] = "2.0.{0}.1".format(-WNF.cm_disc)
info['cm_disc'] = WNF.cm_disc
info['cm_field_knowl'] = nf_display_knowl(
info['cm_field'], getDBConnection(),
field_pretty(info['cm_field']))
info['cm_field_url'] = url_for("number_fields.by_label",
label=info["cm_field"])
if WNF.is_cm is None or WNF.is_cm == -1:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm == 1:
s = 'Yes<br>'
else:
s = 'No<br>'
properties2.append(('CM', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev, dict) and len(alev.keys()) > 0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if (level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6', '')
if poly != '':
d, monom, coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(len(coeffs)):
c = QQ(coeffs[i])
s = ""
if d > 1 and i > 0 and c > 0:
s = "+"
if c < 0:
s = "-"
if c.denominator() > 1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(
abs(c.numerator()), c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]
b = monom[i][1]
if a == 1:
a = ""
if b == 1:
b = ""
if a == 0 and b != 0:
s += "E_6^{{ {0} }}(z)".format(b)
elif b == 0 and a != 0:
s += "E_4^{{ {0} }}(z)".format(a)
else:
s += "E_4^{{ {0} }}(z) \cdot E_6^{{ {1} }}(z)".format(a, b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
# cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + '&label=' + str(label) # never used
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if (label_other != label):
s = 'Modular form '
if character:
s += newform_label(level, weight, character, label_other)
else:
s += newform_label(level, weight, 1, label_other)
url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s += newform_label(level, weight, character, label)
else:
s += newform_label(level, weight, 1, label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label)
if WNF.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_degree):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight == 2 and WNF.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_available_prec()
return info
def set_info_for_modular_form_space(level=None,
weight=None,
character=None,
label=None,
**kwds):
r"""
Set information about a space of modular forms.
"""
info = dict()
info['level'] = level
info['weight'] = weight
info['character'] = character
emf_logger.debug("info={0}".format(info))
if (level > N_max_db or weight > k_max_db):
info['error'] = "Currently not available"
WMFS = None
if level <= 0:
info['error'] = "Got wrong level: %s " % level
return info
try:
if use_db:
WMFS = WebModFormSpace(weight, level, character, use_db=True)
else:
WMFS = WebModFormSpace(weight, level, character)
if 'download' in info and 'tempfile' in info:
WNF._save_to_file(info['tempfile'])
info['filename'] = str(weight) + '-' + str(level) + '-' + str(
character) + '-' + label + '.sobj'
return info
except RuntimeError:
info['error'] = "Sage error: Could not construct the desired space!"
if WMFS.level() == 1:
info['group'] = "\( \mathrm{SL}_{2}(\mathbb{Z})\)"
else:
info['group'] = "\( \Gamma_{{0}}( {0} ) \)".format(WMFS.level())
if character == 0:
info['name_new'] = "\(S_{ %s }^{new}(%s) \)" % (WMFS.weight(),
WMFS.level())
info['name_old'] = "\(S_{ %s }^{old}(%s) \)" % (WMFS.weight(),
WMFS.level())
else:
conrey_char = WMFS.conrey_character()
conrey_char_name = WMFS.conrey_character_name()
info['conrey_character_name'] = '\( ' + conrey_char_name + '\)'
info['character_url'] = url_character(type='Dirichlet',
modulus=WMFS.level(),
number=conrey_char.number())
info['name_new'] = "\(S_{ %s }^{new}(%s,%s) \)" % (
WMFS.weight(), WMFS.level(), conrey_char_name)
info['name_old'] = "\(S_{ %s }^{old}(%s,%s) \)" % (
WMFS.weight(), WMFS.level(), conrey_char_name)
info['dimension_cusp_forms'] = WMFS.dimension_cusp_forms()
info['dimension_mod_forms'] = WMFS.dimension_modular_forms()
info['dimension_new_cusp_forms'] = WMFS.dimension_new_cusp_forms()
info['dimension_newspace'] = WMFS.dimension_newspace()
info['dimension_oldspace'] = WMFS.dimension_oldspace()
info['dimension'] = WMFS.dimension()
info['galois_orbits'] = WMFS.get_all_galois_orbit_info()
lifts = list()
if WMFS.dimension() == 0: # we don't need to work with an empty space
info['sturm_bound'] = 0
info['new_decomposition'] = ''
info['is_empty'] = 1
lifts.append(('Half-Integral Weight Forms', '/ModularForm/Mp2/Q'))
lifts.append(('Siegel Modular Forms', '/ModularForm/GSp4/Q'))
info['lifts'] = lifts
return info
info['sturm_bound'] = WMFS.sturm_bound()
info['new_decomposition'] = WMFS.print_galois_orbits()
emf_logger.debug("new_decomp={0}".format(info['new_decomposition']))
info['nontrivial_new'] = len(info['new_decomposition'])
## we try to catch well-known bugs...
info['old_decomposition'] = "n/a"
if level < N_max_comp:
try:
O = WMFS.print_oldspace_decomposition()
info['old_decomposition'] = O
except:
emf_logger.critical("Error in computing oldspace decomposition")
O = []
info['old_decomposition'] = "n/a"
(A, B, C) = sys.exc_info()
# build an error message...
errtype = A.__name__
errmsg = B
s = "%s: %s at:" % (errtype, errmsg)
next = C.tb_next
while (next):
ln = next.tb_lineno
filen = next.tb_frame.f_code.co_filename
s += "\n line no. %s in file %s" % (ln, filen)
next = next.tb_next
info['error_note'] = "Could not construct oldspace!\n" + s
# properties for the sidebar
prop = []
if WMFS._cuspidal == 1:
prop = [('Dimension newforms', [info['dimension_newspace']])]
prop.append(('Dimension oldforms', [info['dimension_oldspace']]))
else:
prop = [('Dimension modular forms', [info['dimension_mod_forms']])]
prop.append(('Dimension cusp forms', [info['dimension_cusp_forms']]))
prop.append(('Sturm bound', [WMFS.sturm_bound()]))
info['properties2'] = prop
## Make parent spaces of S_k(N,chi) for the sidebar
par_lbl = '\( S_{*} (\Gamma_0(' + str(level) + '),\cdot )\)'
par_url = '?level=' + str(level)
parents = [[par_lbl, par_url]]
par_lbl = '\( S_{k} (\Gamma_0(' + str(level) + '),\cdot )\)'
par_url = '?level=' + str(level) + '&weight=' + str(weight)
parents.append((par_lbl, par_url))
info['parents'] = parents
if 'character' in info:
info['character_order'] = WMFS.character_order()
info['character_conductor'] = WMFS.character_conductor()
friends = list()
lifts = list()
if (('label' not in info) and info['old_decomposition'] != 'n/a'):
O = WMFS.oldspace_decomposition()
try:
for (old_level, chi, mult, d) in O:
if chi != 0:
s = "\(S_{%s}(\Gamma_0(%s),\chi_{%s}) \) " % (
weight, old_level, chi)
friends.append((s, '?weight=' + str(weight) + '&level=' +
str(old_level) + '&character=' + str(chi)))
else:
s = "\(S_{%s}(\Gamma_0(%s)) \) " % (weight, old_level)
friends.append((s, '?weight=' + str(weight) + '&level=' +
str(old_level) + '&character=' + str(0)))
except:
pass
info['friends'] = friends
lifts.append(('Half-Integral Weight Forms', '/ModularForm/Mp2/Q'))
lifts.append(('Siegel Modular Forms', '/ModularForm/GSp4/Q'))
info['lifts'] = lifts
return info
def set_info_for_gamma1(level, weight, weight2=None):
dimension_table_name = WebModFormSpace._dimension_table_name
if weight != None and weight2 > weight:
w1 = weight
w2 = weight2
else:
w1 = weight
w2 = weight
table = {'galois_orbit': {}, 'galois_orbits_reps': {}, 'cells': {}}
table['weights'] = range(w1, w2 + 1)
emf_logger.debug("dimension table name={0}".format(dimension_table_name))
db_dim = getDBConnection()['modularforms2'][dimension_table_name]
s = {
'level': int(level),
'weight': {
"$lt": int(w2 + 1),
"$gt": int(w1 - 1)
},
'cchi': {
"$exists": True
}
}
q = db_dim.find(s).sort([('cchi', int(1)), ('weight', int(1))])
if q.count() == 0:
emf_logger.debug("No spaces in the database!")
flash(
'The database does not currently contain any spaces matching these parameters. Please try again!'
)
return None #'error':'The database does not currently contain any spaces matching these parameters!'}
else:
table['maxGalCount'] = 1
for r in q:
xi = r['cchi']
orbit = r['character_orbit']
k = r['weight']
## This is probably still quicker if it is in the database
parity = r.get('character_parity', 'n/a')
if parity == 'n/a':
chi = ConreyCharacter(level, xi)
if chi.is_odd():
parity = -1
elif chi.is_even():
parity = 1
else:
emf_logger.critical(
"Could not determine the parity of ConreyCharacter({0},{1})"
.format(xi, level))
trivial_trivially = ""
if parity != 'n/a':
if k % 2 == (1 +
parity) / 2: # is space empty because of parity?
trivial_trivially = "yes"
else:
trivial_trivially = ""
if parity == 1:
parity = 'even'
elif parity == -1:
parity = 'odd'
d = r.get('d_newf', "n/a")
indb = r.get('in_wdb', 0)
if d == 0:
indb = 1
if indb:
url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=k,
character=xi)
else:
url = ''
if not table['galois_orbits_reps'].has_key(xi):
table['galois_orbits_reps'][xi] = {
'head':
"\(\chi_{{{0}}}({1},\cdot) \)".format(
level, xi), # yes, {{{ is required
'chi':
"{0}".format(xi),
'url':
url_for('characters.render_Dirichletwebpage',
modulus=level,
number=xi),
'parity':
parity
}
table['galois_orbit'][xi] = [
{
#'head' : "\(\chi_{{{0}}}({1},\cdot) \)".format(level,xci), # yes, {{{ is required
## 'head' : "\(S_{{{0}}}({1},\chi({2}, \cdot) ) \)".format(weight,level,xci), # yes, {{{ is required
## 'head' : "\(S_{{{0}}}(\chi({1}, \cdot) ) \)".format(weight,xci), # yes, {{{ is required
'head':
r"\(S_{{{0}}}(\chi_{{{1}}}({2}, \cdot)) \)".format(
weight, level, xci), # yes, {{{ is required
# 'head' : "\({0}\)".format(xci),
'chi':
"{0}".format(xci),
# 'url': url_for('characters.render_Dirichletwebpage', modulus=level, number=xci)
'url':
url_for('emf.render_elliptic_modular_forms',
level=level,
weight=k,
character=xci) if indb else ''
} for xci in orbit
]
if len(orbit) > table['maxGalCount']:
table['maxGalCount'] = len(orbit)
table['cells'][xi] = {}
table['cells'][xi][k] = {
'N': level,
'k': k,
'chi': xi,
'url': url,
'dim': d,
'trivial_trivially': trivial_trivially,
}
table['galois_orbits_reps_numbers'] = table['galois_orbits_reps'].keys()
table['galois_orbits_reps_numbers'].sort()
#emf_logger.debug("Table:{0}".format(table))
return table
