def compare_with_db(self, field=None):
lab = self.dbdata['label']
f = WebHMF.by_label(lab)
if f==None:
print("No Hilbert newform in the database has label %s" % lab)
return False
if field==None:
field = HilbertNumberField(self.dbdata['field_label'])
agree = True
for key in self.dbdata.keys():
if key in ['is_base_change', 'is_CM']:
continue
if key=='hecke_eigenvalues':
if self.dbdata[key]!=f.dbdata[key]:
agree = False
print("Inconsistent data for HMF %s in field %s" % (lab,key))
print("self has %s entries, \ndb has %s entries" % (len(self.dbdata[key]),len(f.dbdata[key])))
print("Entries differ at indices %s" % [i for i in range(len(self.dbdata[key])) if self.dbdata[key][i]!=f.dbdata[key][i]])
elif key=='level_ideal':
if self.dbdata[key]!=f.dbdata[key]:
I = field.ideal_from_str(f.dbdata['level_ideal'])[2]
J = field.ideal_from_str(self.dbdata['level_ideal'])[2]
if I==J:
print("OK, these are the same ideal")
else:
agree = False
print("These are different ideals!")
else:
if self.dbdata[key]!=f.dbdata[key]:
agree = False
print("Inconsistent data for HMF %s in field %s" % (lab,key))
return agree
def create_from_data_string(self, label_or_field, L):
"""Takes an input line L from a raw data file and constructs the
associated HMF object with given base field.
String sample:
<[31, 31, w + 12], "a", [-3, -2, 2, 4, -4, ...]>,
"""
data = self.dbdata = {}
if isinstance(label_or_field, str):
label = label_or_field
data['field_label'] = label
F = HilbertNumberField(label)
if not F:
raise ValueError("No Hilbert number field with label %s is in the database" % label)
elif label_or_field == None:
raise ValueError("Must specify a valid field label")
else: # we were passed a HilbertNumberField already
F = label_or_field
data['field_label'] = F.label
#print("data['field_label'] = %s" % data['field_label'])
# The level
i = L.find('[')
j = L.find(']')
data['level_ideal'] = L[i:j+1]
#print("data['level_ideal'] = %s" % data['level_ideal'])
N, n, alpha = data['level_ideal'][1:-1].split(',')
data['level_norm'] = int(N)
#print("data['level_norm'] = %s" % data['level_norm'])
level = F.ideal_from_str(data['level_ideal'])[2]
#print("level = %s" % level)
data['level_label'] = F.ideal_label(level)
#print("data['level_label'] = %s" % data['level_label'])
# The weight
data['parallel_weight'] = int(2)
data['weight'] = str([data['parallel_weight']] * F.degree())
weight = [2] * F.degree()
# The label
i = L.find('"')
j = L.find('"', i+1)
data['label_suffix'] = L[i+1:j].replace(" ","")
data['label'] = construct_full_label(data['field_label'],
weight,
data['level_label'],
data['label_suffix'])
data['short_label'] = '-'.join([data['level_label'], data['label_suffix']])
#print("data['label'] = %s" % data['label'] )
#print("data['short_label'] = %s" % data['short_label'] )
# The hecke polynomial and degree
if 'x' in L:
# non-rational
i = L.find("x")
j = L.find(i+1,",")
data['hecke_polynomial'] = pol = L[i:j]
data['dimension'] = int(1)
x = polygen(QQ)
hpol = x.parent()(str(pol))
data['dimension'] = int(hpol.degree())
else:
# rational
data['hecke_polynomial'] = 'x'
data['dimension'] = int(1)
i = L.rfind("[")
j = L.rfind("]")
data['hecke_eigenvalues'] = L[i+1:j].replace(" ","").split(",")
data['hecke_eigenvalues'] = [unicode(s) for s in data['hecke_eigenvalues']]
#print("hecke_eigenvalues = %s..." % data['hecke_eigenvalues'][:20])
# Find (some of the) AL-eigenvalues
BP = level.prime_factors()
BP_indices = [F.prime_index(P) for P in BP]
print("BP_indices = %s" % BP_indices)
BP_exponents = [level.valuation(P) for P in BP]
#print("BP_exponents = %s" % BP_exponents)
AL_eigs = [int(data['hecke_eigenvalues'][k]) for k in BP_indices]
#print("AL_eigs = %s" % AL_eigs)
if not all([(e==1 and eig in [-1,1]) or (eig==0)
for e,eig in zip(BP_exponents,AL_eigs)]):
print("Some bad AL-eigenvalues found")
# NB the following will put 0 for the eigenvalue for primes
# whose quare divides the level; this will need fixing later.
data['AL_eigenvalues'] = [[F.primes[k],data['hecke_eigenvalues'][k]] for k in BP_indices]
data['is_CM'] = '?'
data['is_base_change'] = '?'
