def pol_string_to_list(pol, deg=None, var=None):
if var is None:
from lmfdb.hilbert_modular_forms.hilbert_field import findvar
var = findvar(pol)
if not var:
var = 'a'
pol = PolynomialRing(QQ, var)(str(pol))
if deg is None:
fill = 0
else:
fill = deg - pol.degree() - 1
return [str(c) for c in pol.coefficients(sparse=False)] + ['0'] * fill
def pol_string_to_list(pol, deg=None, var=None):
if var is None:
from lmfdb.hilbert_modular_forms.hilbert_field import findvar
var = findvar(pol)
if not var:
var = 'a'
pol = PolynomialRing(QQ, var)(str(pol))
if deg is None:
fill = 0
else:
fill = deg - pol.degree() - 1
return [str(c) for c in pol.coefficients(sparse=False)] + ['0']*fill
def checkprimes(label):
Fdata = get_Fdata(label)
gen_name = findvar(Fdata['ideals'])
WebF = get_WNF(label, gen_name)
F = WebF.K()
ideals = niceideals(F, Fdata['ideals'])
primes = niceideals(F, Fdata['primes'])
F = HilbertNumberField(label)
L = []
for prhnf, prideal, prlabel in primes:
ideal = F.ideal(prlabel)
if ideal != prideal:
L.append(prlabel)
return L
def checkprimes(label):
Fdata = get_Fdata(label)
gen_name = findvar(Fdata['ideals'])
WebF = get_WNF(label, gen_name)
F = WebF.K()
# ideals = niceideals(F, Fdata['ideals']) # never used
primes = niceideals(F, Fdata['primes'])
F = HilbertNumberField(label)
L = []
for prhnf,prideal,prlabel in primes:
ideal = F.ideal(prlabel)
if ideal != prideal:
L.append(prlabel)
return L
def fldlabel2conjdata(label):
data = {}
Fdata = get_Fdata(label)
gen_name = findvar(Fdata['ideals'])
WebF = get_WNF(label, gen_name)
F = WebF.K()
data['F'] = F
auts = F.automorphisms()
if len(auts) == 1: #no nontrivial automorphism, nothing to do
return None
auts = [g for g in auts if not g.is_identity()]
data['auts'] = auts
ideals = niceideals(F, Fdata['ideals'])
data['ideals'] = ideals
cideals = conjideals(ideals, auts)
data['conjideals'] = cideals
primes = niceideals(F, Fdata['primes'])
data['primes'] = primes
cprimes = conjideals(primes, auts)
data['conjprimes'] = cprimes
return data
def fldlabel2conjdata(label):
data = {}
Fdata = get_Fdata(label)
gen_name = findvar(Fdata['ideals'])
WebF = get_WNF(label, gen_name)
F = WebF.K()
data['F'] = F
auts = F.automorphisms()
if len(auts) == 1: #no nontrivial automorphism, nothing to do
return None
auts = [g for g in auts if not g.is_identity()]
data['auts'] = auts
ideals = niceideals(F, Fdata['ideals'])
data['ideals'] = ideals
cideals = conjideals(ideals, auts)
data['conjideals'] = cideals
primes = niceideals(F, Fdata['primes'])
data['primes'] = primes
cprimes = conjideals(primes, auts)
data['conjprimes'] = cprimes
return data
def render_hmf_webpage(**args):
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = get_hmf(label)
if data is None:
flash_error(
"%s is not a valid Hilbert modular form label. It must be of the form (number field label) - (level label) - (orbit label) separated by dashes, such as 2.2.5.1-31.1-a",
args['label'])
return search_input_error()
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 50
hmf_field = get_hmf_field(data['field_label'])
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [('Modular form to Magma',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='magma')),
('Eigenvalues to Sage',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='sage'))]
# figure out friends
# first try to see if there is an instance of this HMF on Lfun db
url = 'ModularForm/GL2/TotallyReal/{}/holomorphic/{}'.format(
info['field_label'], info['label'])
Lfun = get_lfunction_by_url(url)
if Lfun:
instances = get_instances_by_Lhash_and_trace_hash(
Lfun['Lhash'], Lfun['degree'], Lfun['trace_hash'])
# This will also add the EC/G2C, as this how the Lfun was computed
info['friends'] = names_and_urls(instances, exclude={url})
info['friends'] += [('L-function',
url_for("l_functions.l_function_hmf_page",
field=info['field_label'],
label=info['label'],
character='0',
number='0'))]
else:
# if there is no instance
# old code
if hmf_field['narrow_class_no'] == 1 and nf.disc(
)**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page",
field=info['field_label'],
label=info['label'],
character='0',
number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db.ec_nfcurves.lookup(label + '1')
if ec_from_hmf is None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'],
url_for("ecnf.show_ecnf_isoclass",
nf=lab[0],
conductor_label=lab[1],
class_label=lab[2]))]
bread = [("Modular Forms", url_for('modular_forms')),
('Hilbert Modular Forms',
url_for(".hilbert_modular_form_render_webpage")),
('%s' % data['label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_dims = db.hmf_forms.search(
{
'field_label': data['field_label'],
'level_ideal': data['level_ideal']
},
projection='dimension')
info['newspace_dimension'] = sum(forms_dims)
# Get hecke_polynomial, hecke_eigenvalues and AL_eigenvalues
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
info['numeigs'] = numeigs
hecke_pol = data['hecke_polynomial']
eigs = map(str, data['hecke_eigenvalues'])
eigs = eigs[:min(len(eigs), numeigs)]
AL_eigs = data['AL_eigenvalues']
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{
'eigenvalue': add_space_if_positive(teXify_pol(eigs[i])),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]
} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = "\(" + teXify_pol(hecke_pol) + "\)"
if not AL_eigs: # empty list
if data['level_norm'] == 1: # OK, no bad primes
info['AL_eigs'] = 'none'
else: # not OK, AL eigs are missing
info['AL_eigs'] = 'missing'
else:
info['AL_eigs'] = [{
'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]
} for al in data['AL_eigenvalues']]
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len <= 300)
info['display_eigs'] = display_eigs
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label']),
('Dimension', '%s' % data['dimension']), ('CM', is_CM),
('Base change', is_base_change)]
return render_template("hilbert_modular_form.html",
downloads=info["downloads"],
info=info,
properties=properties,
credit=hmf_credit,
title=t,
bread=bread,
friends=info['friends'],
learnmore=learnmore_list())
def render_hmf_webpage(**args):
C = getDBConnection()
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = C.hmfs.forms.find_one({'label': label})
if data is None:
return "No such form"
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
hmf_field = C.hmfs.fields.find_one({'label': data['field_label']})
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [
('Download to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
('Download to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
]
if hmf_field['narrow_class_no'] == 1:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'], url_for("ecnf.show_ecnf_isoclass", nf=lab[0], conductor_label=lab[1], class_label=lab[2]))]
bread = [('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")), ('%s' % data[
'label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = C.hmfs.forms.find(
{'field_label': data['field_label'], 'level_ideal': data['level_ideal']})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
w = polygen(QQ, 'w')
e = polygen(QQ, 'e')
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{'eigenvalue': teXify_pol(eigs[i]),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = teXify_pol(info['hecke_polynomial'])
if 'AL_eigenvalues_fixed' in data:
if data['AL_eigenvalues_fixed'] == 'done':
info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
info['AL_eigs_count'] = len(info['AL_eigs']) != 0
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len<=300)
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
for eig in info['AL_eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label_suffix']),
('Dimension', '%s' % data['dimension']),
('CM', is_CM),
('Base change', is_base_change)
]
return render_template("hilbert_modular_form.html", downloads=info["downloads"], info=info, properties2=properties2, credit=hmf_credit, title=t, bread=bread, friends=info['friends'], learnmore=learnmore_list())
def render_hmf_webpage(**args):
C = getDBConnection()
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = C.hmfs.forms.find_one({'label': label})
if data is None:
return "No such form"
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
hmf_field = C.hmfs.fields.find_one({'label': data['field_label']})
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [('Download to Magma',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='magma')),
('Download to Sage',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='sage'))]
if hmf_field['narrow_class_no'] == 1 and nf.disc(
)**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page",
field=info['field_label'],
label=info['label'],
character='0',
number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'],
url_for("ecnf.show_ecnf_isoclass",
nf=lab[0],
conductor_label=lab[1],
class_label=lab[2]))]
bread = [('Hilbert Modular Forms',
url_for(".hilbert_modular_form_render_webpage")),
('%s' % data['label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = C.hmfs.forms.find({
'field_label': data['field_label'],
'level_ideal': data['level_ideal']
})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
w = polygen(QQ, 'w')
e = polygen(QQ, 'e')
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{
'eigenvalue': teXify_pol(eigs[i]),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]
} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = teXify_pol(info['hecke_polynomial'])
if 'AL_eigenvalues_fixed' in data:
if data['AL_eigenvalues_fixed'] == 'done':
info['AL_eigs'] = [{
'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]
} for al in data['AL_eigenvalues']]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
info['AL_eigs_count'] = len(info['AL_eigs']) != 0
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len <= 300)
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
for eig in info['AL_eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label']),
('Dimension', '%s' % data['dimension']), ('CM', is_CM),
('Base change', is_base_change)]
return render_template("hilbert_modular_form.html",
downloads=info["downloads"],
info=info,
properties2=properties2,
credit=hmf_credit,
title=t,
bread=bread,
friends=info['friends'],
learnmore=learnmore_list())
def render_hmf_webpage(**args):
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = get_hmf(label)
if data is None:
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid Hilbert modular form label. It must be of the form (number field label) - (level label) - (orbit label) separated by dashes, such as 2.2.5.1-31.1-a" % args['label']), "error")
return search_input_error()
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 50
hmf_field = get_hmf_field(data['field_label'])
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [
('Modular form to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
('Eigenvalues to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
]
# figure out friends
# first try to see if there is an instance of this HMF on Lfun db
url = 'ModularForm/GL2/TotallyReal/{}/holomorphic/{}'.format(
info['field_label'],
info['label'])
Lfun = get_lfunction_by_url(url)
if Lfun:
instances = get_instances_by_Lhash_and_trace_hash(Lfun['Lhash'],
Lfun['degree'],
Lfun['trace_hash'])
# This will also add the EC/G2C, as this how the Lfun was computed
info['friends'] = names_and_urls(instances, exclude={url})
info['friends'] += [('L-function',
url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
else:
# if there is no instance
# old code
if hmf_field['narrow_class_no'] == 1 and nf.disc()**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db.ec_nfcurves.lookup(label + '1')
if ec_from_hmf is None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'], url_for("ecnf.show_ecnf_isoclass", nf=lab[0], conductor_label=lab[1], class_label=lab[2]))]
bread = [("Modular Forms", url_for('modular_forms')), ('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")),
('%s' % data['label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_dims = db.hmf_forms.search({'field_label': data['field_label'], 'level_ideal': data['level_ideal']}, projection='dimension')
info['newspace_dimension'] = sum(forms_dims)
# Get hecke_polynomial, hecke_eigenvalues and AL_eigenvalues
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
info['numeigs'] = numeigs
hecke_pol = data['hecke_polynomial']
eigs = map(str, data['hecke_eigenvalues'])
eigs = eigs[:min(len(eigs), numeigs)]
AL_eigs = data['AL_eigenvalues']
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{'eigenvalue': add_space_if_positive(teXify_pol(eigs[i])),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = web_latex_split_on_pm(teXify_pol(hecke_pol))
if not AL_eigs: # empty list
if data['level_norm']==1: # OK, no bad primes
info['AL_eigs'] = 'none'
else: # not OK, AL eigs are missing
info['AL_eigs'] = 'missing'
else:
info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len<=300)
info['display_eigs'] = display_eigs
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label']),
('Dimension', '%s' % data['dimension']),
('CM', is_CM),
('Base change', is_base_change)
]
return render_template("hilbert_modular_form.html", downloads=info["downloads"], info=info, properties2=properties2, credit=hmf_credit, title=t, bread=bread, friends=info['friends'], learnmore=learnmore_list())
def render_hmf_webpage(**args):
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = get_hmf(label)
if data is None:
flash(
Markup(
"Error: <span style='color:black'>%s</span> is not a valid Hilbert modular form label. It must be of the form (number field label) - (level label) - (orbit label) separated by dashes, such as 2.2.5.1-31.1-a"
% args['label']), "error")
return search_input_error()
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
hmf_field = get_hmf_field(data['field_label'])
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [('Download to Magma',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='magma')),
('Download to Sage',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='sage'))]
if hmf_field['narrow_class_no'] == 1 and nf.disc(
)**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page",
field=info['field_label'],
label=info['label'],
character='0',
number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'],
url_for("ecnf.show_ecnf_isoclass",
nf=lab[0],
conductor_label=lab[1],
class_label=lab[2]))]
bread = [('Hilbert Modular Forms',
url_for(".hilbert_modular_form_render_webpage")),
('%s' % data['label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = db_search().find(
{
'field_label': data['field_label'],
'level_ideal': data['level_ideal']
}, {'dimension': True})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
# Get hecke_polynomial, hecke_eigenvalues and AL_eigenvalues
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
info['numeigs'] = numeigs
hecke_pol = data['hecke_polynomial']
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
AL_eigs = data['AL_eigenvalues']
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{
'eigenvalue': teXify_pol(eigs[i]),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]
} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = web_latex_split_on_pm(teXify_pol(hecke_pol))
if not AL_eigs: # empty list
if data['level_norm'] == 1: # OK, no bad primes
info['AL_eigs'] = 'none'
else: # not OK, AL eigs are missing
info['AL_eigs'] = 'missing'
else:
info['AL_eigs'] = [{
'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]
} for al in data['AL_eigenvalues']]
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len <= 300)
info['display_eigs'] = display_eigs
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label']),
('Dimension', '%s' % data['dimension']), ('CM', is_CM),
('Base change', is_base_change)]
return render_template("hilbert_modular_form.html",
downloads=info["downloads"],
info=info,
properties2=properties2,
credit=hmf_credit,
title=t,
bread=bread,
friends=info['friends'],
learnmore=learnmore_list())
def render_hmf_webpage(**args):
C = getDBConnection()
data = None
if 'label' in args:
label = str(args['label'])
data = C.hmfs.forms.find_one({'label': label})
if data is None:
return "No such field"
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
hmf_field = C.hmfs.fields.find_one({'label': data['field_label']})
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [
('Download to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
('Download to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
]
info['friends'] = []
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
# info['learnmore'] = [('Number Field labels',
# url_for("render_labels_page")), ('Galois group
# labels',url_for("render_groups_page")), ('Discriminant
# ranges',url_for("render_discriminants_page"))]
bread = [('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")), ('%s' % data[
'label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
credit = 'Lassina Dembele, Steve Donnelly and <A HREF="http://www.cems.uvm.edu/~voight/">John Voight</A>'
forms_space = C.hmfs.forms.find(
{'field_label': data['field_label'], 'level_ideal': data['level_ideal']})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
w = polygen(QQ, 'w')
e = polygen(QQ, 'e')
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{'eigenvalue': teXify_pol(eigs[i]),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = teXify_pol(info['hecke_polynomial'])
if 'AL_eigenvalues_fixed' in data:
if data['AL_eigenvalues_fixed'] == 'done':
info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
info['AL_eigs_count'] = len(info['AL_eigs']) != 0
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
for eig in info['AL_eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base Field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level Norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label_suffix']),
('Dimension', '%s' % data['dimension']),
('CM', is_CM),
('Base Change', is_base_change)
]
return render_template("hilbert_modular_form.html", downloads=info["downloads"], info=info, properties2=properties2, credit=credit, title=t, bread=bread, friends=info['friends'])