def print_list_of_coefficients(info):
r"""
Print a table of Fourier coefficients in the requested format
"""
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
prec = my_get(info, 'prec', 12, int) # number of digits
bitprec = my_get(info, 'bitprec', 12, int) # number of digits
character = my_get(info, 'character', '', str) # int(info.get('weight',0))
if character == '':
character = 0
label = info.get('label', '')
print "--------------"
if label == '' or level == -1 or weight == -1:
return "Need to specify a modular form completely!!"
WMFS = WebModFormSpace(N=level, k=weight, chi=character)
if not WMFS:
return ""
if ('number' in info):
number = int(info['number'])
else:
number = max(WMFS.sturm_bound() + 1, 20)
FS = list()
if (label is not None):
FS.append(WMFS.f(label))
else:
for a in WMFS.labels():
FS.append(WMFS.f(a))
shead = "Cusp forms of weight " + str(weight) + "on \(" + latex(
WMFS.group()) + "\)"
s = ""
if ((character is not None) and (character > 0)):
s = s + " and character \( \chi_{" + str(character) + "}\)"
# s="<table><tr><td>"
coefs = ""
for F in FS:
if len(FS) > 1:
if info['format'] == 'html':
coefs += F.label()
else:
coefs += F.label()
coefs += print_coefficients_for_one_form(F,
number,
info['format'],
bitprec=bitprec)
ss = coefs
return ss
def print_list_of_coefficients(info):
r"""
Print a table of Fourier coefficients in the requested format
"""
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
prec = my_get(info, 'prec', 12, int) # number of digits
character = my_get(info, 'character', '', str) # int(info.get('weight',0))
if character == '':
character = 0
label = info.get('label', '')
print "--------------"
if label == '' or level == -1 or weight == -1:
return "Need to specify a modular form completely!!"
WMFS = WebModFormSpace(N = level, k = weight, chi = character)
if not WMFS:
return ""
if('number' in info):
number = int(info['number'])
else:
number = max(WMFS.sturm_bound() + 1, 20)
if('prec' in info):
bprec = int(ceil(prec * 3.4))
else:
bprec = 53
FS = list()
if(label is not None):
FS.append(WMFS.f(label))
else:
for a in WMFS.labels():
FS.append(WMFS.f(a))
shead = "Cusp forms of weight " + str(weight) + "on \(" + latex(WMFS.group()) + "\)"
s = ""
if((character is not None) and (character > 0)):
s = s + " and character \( \chi_{" + str(character) + "}\)"
# s="<table><tr><td>"
coefs = ""
for F in FS:
if len(FS) > 1:
if info['format'] == 'html':
coefs += F.label()
else:
coefs += F.label()
coefs += print_coefficients_for_one_form(F, number, info['format'])
ss = coefs
return ss
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_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 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
