def _check(k, j):
M = vvsmf(j, k, prec)
if M.dimension() > 0:
self.assertEqual(M.dimension(), len(M.basis()))
_chply = M.hecke_charpoly(2)
for cply, _ in _chply.factor():
K = NumberField(cply, names="a")
a = K.gens()[0]
f = M.eigenform_with_eigenvalue_t2(a)
self.assert_hecke_eigen_values(f)
def relation(wt, data_directory=None):
'''For a given weight wt, this funciton returns a dict whose set of keys
is equal to a set of instances of ConstMul with weight wt.
Its value is a rational number. This dictionary represents a releation
among keys.
'''
wts = (24, 26, 27, 29)
if wt not in wts:
raise ValueError("The weight must be in %s" % (wts,))
prec = 6
M = vvsmf(10, wt, prec, data_directory=data_directory)
mul_consts = M._basis_const_base([])
basis_consts = list(M._basis_const())
another_const = [c for c in mul_consts if c not in basis_consts][0]
f = another_const.calc_form_from_dependencies_depth_1(
prec, M._calculator.forms_dict(prec))
coeffs = list(M._to_vector(f)) + [QQ(-1)]
_gcd = gcd(coeffs)
coeffs = [a / _gcd for a in coeffs]
return {c: a for a, c in zip(coeffs, basis_consts + [another_const])}
