def FIELD(label):
nf = WebNumberField(label, gen_name=special_names.get(label, 'a'))
nf.parse_NFelt = lambda s: nf.K()([QQ(c.encode()) for c in s.split(",")])
nf.latex_poly = web_latex(nf.poly())
return nf
def render_bmf_space_webpage(field_label, level_label):
info = {}
t = "Bianchi modular forms of level %s over %s" % (level_label,
field_label)
credit = bianchi_credit
bread = [('Bianchi modular forms', url_for(".index")),
(field_pretty(field_label),
url_for(".render_bmf_field_dim_table_gl2",
field_label=field_label)), (level_label, '')]
friends = []
properties2 = []
if not field_label_regex.match(field_label):
info[
'err'] = "%s is not a valid label for an imaginary quadratic field" % field_label
else:
pretty_field_label = field_pretty(field_label)
if not db_dims().find({'field_label': field_label}):
info[
'err'] = "no dimension information exists in the database for field %s" % pretty_field_label
else:
t = "Bianchi Modular Forms of level %s over %s" % (
level_label, pretty_field_label)
data = db_dims().find({
'field_label': field_label,
'level_label': level_label
})
nres = data.count()
if nres == 0:
info[
'err'] = "no dimension information exists in the database for level %s and field %s" % (
level_label, pretty_field_label)
else:
data = data.next()
info['label'] = data['label']
nf = WebNumberField(field_label)
info['base_galois_group'] = nf.galois_string()
info['field_label'] = field_label
info['pretty_field_label'] = pretty_field_label
info['level_label'] = level_label
info['level_norm'] = data['level_norm']
info['field_degree'] = nf.degree()
info['field_classno'] = nf.class_number()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info['field_knowl'] = nf_display_knowl(field_label,
getDBConnection(),
pretty_field_label)
w = 'i' if nf.disc() == -4 else 'a'
L = nf.K().change_names(w)
alpha = L.gen()
info['field_gen'] = latex(alpha)
I = ideal_from_label(L, level_label)
info['level_gen'] = latex(I.gens_reduced()[0])
info['level_fact'] = latex(I.factor())
dim_data = data['gl2_dims']
weights = dim_data.keys()
weights.sort(key=lambda w: int(w))
for w in weights:
dim_data[w]['dim'] = dim_data[w]['cuspidal_dim']
info['dim_data'] = dim_data
info['weights'] = weights
info['nweights'] = len(weights)
newdim = data['gl2_dims']['2']['new_dim']
newforms = db_forms().find({
'field_label': field_label,
'level_label': level_label
}).sort('label_suffix', ASCENDING)
info['nfdata'] = [{
'label':
f['short_label'],
'url':
url_for(".render_bmf_webpage",
field_label=f['field_label'],
level_label=f['level_label'],
label_suffix=f['label_suffix']),
'wt':
f['weight'],
'dim':
f['dimension'],
'sfe':
"+1" if f['sfe'] == 1 else "-1",
'bc':
bc_info(f['bc']),
'cm':
cm_info(f['CM']),
} for f in newforms]
info['nnewforms'] = len(info['nfdata'])
properties2 = [('Base field', pretty_field_label),
('Level', info['level_label']),
('Norm', str(info['level_norm'])),
('New dimension', str(newdim))]
friends = [('Newform {}'.format(f['label']), f['url'])
for f in info['nfdata']]
return render_template("bmf-space.html",
info=info,
credit=credit,
title=t,
bread=bread,
properties2=properties2,
friends=friends)
def FIELD(label):
nf = WebNumberField(label, gen_name=special_names.get(label, 'a'))
nf.parse_NFelt = lambda s: nf.K()([QQ(str(c)) for c in s])
return nf