def friends(self):
from lmfdb.lfunctions.LfunctionDatabase import get_lfunction_by_url
f = []
cglink = url_character(type=self.type,
number_field=self.nflabel,
modulus=self.modlabel)
f.append(("Character group", cglink))
if self.nflabel:
f.append(('Number field', '/NumberField/' + self.nflabel))
if self.type == 'Dirichlet' and self.chi.is_primitive(
) and self.conductor < 10000:
url = url_character(type=self.type,
number_field=self.nflabel,
modulus=self.modlabel,
number=self.numlabel)
if get_lfunction_by_url(url[1:]):
f.append(('L-function', '/L' + url))
else:
if self.conductor == 1:
f.append(('L-function', '/L/Riemann'))
if self.type == 'Dirichlet':
f.append(('Sato-Tate group', '/SatoTateGroup/0.1.%d' % self.order))
if len(self.vflabel) > 0:
f.append(("Value field", '/NumberField/' + self.vflabel))
return f
def friends(self):
from lmfdb.lfunctions.LfunctionDatabase import get_lfunction_by_url
friendlist = []
cglink = url_character(type=self.type, modulus=self.modulus)
friendlist.append(("Character group", cglink))
gal_orb_link = url_character(type=self.type,
modulus=self.modulus,
orbit_label=self.orbit_label)
friendlist.append(("Character orbit", gal_orb_link))
if self.type == "Dirichlet" and self.isprimitive == bool_string(True):
url = url_character(type=self.type,
number_field=None,
modulus=self.modulus,
number=self.number)
if get_lfunction_by_url(url[1:]):
friendlist.append(('L-function', '/L' + url))
else:
if self.conductor == 1:
friendlist.append(('L-function', '/L/Riemann'))
friendlist.append(
('Sato-Tate group', '/SatoTateGroup/0.1.%d' % self.order))
if len(self.vflabel) > 0:
friendlist.append(("Value field", '/NumberField/' + self.vflabel))
if self.symbol_numerator():
if self.symbol_numerator() > 0:
assoclabel = '2.2.%d.1' % self.symbol_numerator()
else:
assoclabel = '2.0.%d.1' % -self.symbol_numerator()
friendlist.append(
("Associated quadratic field", '/NumberField/' + assoclabel))
label = "%s.%s" % (self.modulus, self.number)
myrep = db.artin_reps.lucky({'Dets': {'$contains': label}})
if myrep is not None:
j = myrep['Dets'].index(label)
artlabel = myrep['Baselabel'] + '.' + num2letters(j + 1)
friendlist.append((
'Artin representation ' + artlabel,
url_for(
'artin_representations.render_artin_representation_webpage',
label=artlabel)))
if self.type == "Dirichlet" and self.isprimitive == bool_string(False):
friendlist.append(('Primitive character ' + self.inducing,
url_for('characters.render_Dirichletwebpage',
modulus=self.conductor,
number=self.indlabel)))
return friendlist
def friends(self):
f = []
cglink = url_character(type=self.type,number_field=self.nflabel,modulus=self.modlabel)
f.append( ("Character Group", cglink) )
if self.nflabel:
f.append( ('Number Field', '/NumberField/' + self.nflabel) )
if self.type == 'Dirichlet' and self.chi.is_primitive() and self.conductor < 10000:
url = url_character(type=self.type, umber_field=self.nflabel, modulus=self.modlabel, number=self.numlabel)
if lmfdb.lfunctions.LfunctionDatabase.getInstanceLdata(url[1:]):
f.append( ('L-function', '/L'+ url) )
if self.type == 'Dirichlet':
f.append( ('Sato-Tate group', '/SatoTateGroup/0.1.%d'%self.order) )
if len(self.vflabel)>0:
f.append( ("Value Field", '/NumberField/' + self.vflabel) )
return f
def __init__(self, data):
# Need to set mf_dim, eis_dim, cusp_dim, new_dim, old_dim
self.__dict__.update(data)
if self.level == 1 or ZZ(self.level).is_prime():
self.factored_level = ''
else:
self.factored_level = ' = ' + ZZ(self.level).factor()._latex_()
self.char_conrey = self.char_labels[0]
self.char_conrey_str = '\chi_{%s}(%s,\cdot)' % (self.level, self.char_conrey)
self.char_conrey_link = url_character(type='Dirichlet', modulus=self.level, number=self.char_conrey)
self.newforms = list(db.mf_newforms.search({'space_label':self.label}, projection=2))
oldspaces = db.mf_subspaces.search({'label':self.label, 'sub_level':{'$ne':self.level}}, ['sub_level', 'sub_char_orbit_index', 'sub_char_labels', 'sub_mult'])
self.oldspaces = [(old['sub_level'], old['sub_char_orbit_index'], old['sub_char_labels'][0], old['sub_mult']) for old in oldspaces]
self.dim_grid = DimGrid.from_db(data)
self.plot = db.mf_newspace_portraits.lookup(self.label, projection = "portrait")
# Properties
self.properties = [('Label',self.label)]
if self.plot is not None:
self.properties += [(None, '<a href="{0}"><img src="{0}" width="200" height="200"/></a>'.format(self.plot))]
self.properties +=[
('Level',str(self.level)),
('Weight',str(self.weight)),
('Character orbit',self.char_orbit_label),
('Rep. character',r'\(%s\)'%self.char_conrey_str),
('Character field',r'\(\Q%s\)' % ('' if self.char_degree==1 else r'(\zeta_{%s})' % self.char_order)),
('Dimension',str(self.dim)),
('Sturm bound',str(self.sturm_bound)),
('Trace bound',str(self.trace_bound))
]
# Breadcrumbs
self.bread = get_bread(level=self.level, weight=self.weight, char_orbit_label=self.char_orbit_label)
# Downloads
self.downloads = [('Download all stored data', url_for('.download_newspace', label=self.label))]
if self.char_labels[0] == 1:
self.trivial_character = True
character_str = "Trivial Character"
if self.dim == 0:
self.dim_str = r"\(%s\)"%(self.dim)
else:
self.minus_dim = self.dim - self.plus_dim
self.dim_str = r"\(%s + %s\)"%(self.plus_dim, self.minus_dim)
else:
self.trivial_character = False
character_str = r"Character \(\chi_{{{level}}}({conrey}, \cdot)\)".format(level=self.level, conrey=self.char_labels[0])
self.dim_str = r"\(%s\)"%(self.dim)
self.title = r"Space of Cuspidal Newforms of Weight %s, Level %s and %s"%(self.weight, self.level, character_str)
self.friends = []
def friends(self):
friendlist = []
cglink = url_character(type=self.type, modulus=self.modulus)
friendlist.append( ("Character group", cglink) )
if self.type == "Dirichlet" and self.isprimitive == bool_string(True):
friendlist.append(
('Sato-Tate group', '/SatoTateGroup/0.1.%d' % self.order)
)
if len(self.vflabel) > 0:
friendlist.append( ("Value field", '/NumberField/' + self.vflabel) )
if self.symbol_numerator():
if self.symbol_numerator() > 0:
assoclabel = '2.2.%d.1' % self.symbol_numerator()
else:
assoclabel = '2.0.%d.1' % -self.symbol_numerator()
friendlist.append(("Associated quadratic field", '/NumberField/' + assoclabel))
if self.type == "Dirichlet" and self.isprimitive == bool_string(False):
friendlist.append(('Primitive orbit '+self.inducing,
url_for('characters.render_Dirichletwebpage', modulus=self.conductor, orbit_label=self.ind_orbit_label)))
return friendlist
def __init__(self, data, space=None, all_m = False, all_n = False):
#TODO validate data
# Need to set level, weight, character, num_characters, degree, has_exact_qexp, has_complex_qexp, hecke_ring_index, is_twist_minimal
# Make up for db_backend currently deleting Nones
for elt in db.mf_newforms.col_type:
if elt not in data:
data[elt] = None
self.__dict__.update(data)
self._data = data
self.hecke_orbit_label = cremona_letter_code(self.hecke_orbit - 1)
if self.level == 1 or ZZ(self.level).is_prime():
self.factored_level = ''
else:
self.factored_level = ' = ' + ZZ(self.level).factor()._latex_()
# We always print analytic conductor with 1 decimal digit
self.analytic_conductor = '%.1f'%(self.analytic_conductor)
self.single_generator = self.hecke_ring_power_basis or (self.dim == 2)
if self.has_inner_twist != 0:
if self.inner_twist_proved:
if len(self.inner_twist == 1):
self.star_twist = 'inner twist'
else:
self.star_twist = 'inner twists'
elif len(self.inner_twist) == 1:
self.star_twist = 'inner twist*'
else:
self.star_twist = 'inner twists*'
self.has_analytic_rank = data.get('analytic_rank') is not None
eigenvals = db.mf_hecke_nf.search({'hecke_orbit_code':self.hecke_orbit_code, 'n':{'$lt':100}}, ['n','an','trace_an'], sort=['n'])
if eigenvals: # this should always be true
self.has_exact_qexp = True
zero = [0] * self.dim
self.qexp = [zero]
self.texp = [0]
for i, ev in enumerate(eigenvals, 1):
if ev['n'] != i:
raise ValueError("Missing eigenvalue")
self.texp.append(ev['trace_an'])
if ev.get('an'):
self.qexp.append(ev['an'])
else:
# only had traces
self.has_exact_qexp = False
self.qexp_prec = len(self.qexp)
self.texp_prec = len(self.texp)
else:
self.has_exact_qexp = False
self.rel_dim = self.dim // self.char_degree
## CC_DATA
self.cqexp_prec = 1001 # Initial estimate for error messages in render_newform_webpage.
# Should get updated in setup_cc_data.
self.has_complex_qexp = False # stub, overwritten by setup_cc_data.
self.char_conrey = self.char_labels[0]
self.char_conrey_str = '\chi_{%s}(%s,\cdot)' % (self.level, self.char_conrey)
self.char_conrey_link = url_character(type='Dirichlet', modulus=self.level, number=self.char_conrey)
if self.has_inner_twist:
self.inner_twist = [(chi,url_character(type='Dirichlet', modulus=self.level, number=chi)) for chi in self.inner_twist]
self.character_label = "\(" + str(self.level) + "\)." + self.char_orbit_label
self.has_further_properties = (self.is_cm != 0 or self.__dict__.get('is_twist_minimal') or self.has_inner_twist != 0 or self.char_orbit_index == 1 and self.level != 1 or self.hecke_cutters)
self.plot = db.mf_newform_portraits.lookup(self.label, projection = "portrait")
# properties box
self.properties = [('Label', self.label)]
if self.plot is not None:
self.properties += [(None, '<a href="{0}"><img src="{0}" width="200" height="200"/></a>'.format(self.plot))]
self.properties += [('Level', str(self.level)),
('Weight', str(self.weight)),
('Character orbit', '%s.%s' % (self.level, self.char_orbit_label))]
if self.is_self_dual != 0:
self.properties += [('Self dual', 'Yes' if self.is_self_dual == 1 else 'No')]
self.properties += [('Analytic conductor', self.analytic_conductor)]
if self.analytic_rank is not None:
self.properties += [('Analytic rank', str(int(self.analytic_rank)))]
self.properties += [('Dimension', str(self.dim))]
if self.projective_image:
self.properties += [('Projective image', '\(%s\)' % self.projective_image_latex)]
if self.artin_degree: # artin_degree > 0
self.properties += [('Artin image size', str(self.artin_degree))]
if self.artin_image:
self.properties += [('Artin image', '\(%s\)' % self.artin_image_display)]
if self.is_self_twist ==1:
if self.is_cm == 1:
disc = ' and '.join([ str(d) for d in self.self_twist_discs if d < 0 ])
self.properties += [('CM discriminant', disc)]
elif self.is_cm == -1:
self.properties += [('CM', 'No')]
if self.weight == 1:
if self.is_rm == 1:
disc = ' and '.join([ str(d) for d in self.self_twist_discs if d > 0 ])
self.properties += [('RM discriminant', disc)]
elif self.is_rm == -1:
self.properties += [('RM', 'No')]
# Breadcrumbs
self.bread = get_bread(level=self.level, weight=self.weight, char_orbit_label=self.char_orbit_label, hecke_orbit=cremona_letter_code(self.hecke_orbit - 1))
self.title = "Newform %s"%(self.label)