def test_wt_20_eigen(self):
N20 = KlingenEisensteinAndCuspForms(20)
pl = N20.hecke_charpoly(2)
x = pl.parent().gens()[0]
pl1 = ((x + Integer(840960)) *
(x ** Integer(2) - Integer(1378464) * x + Integer(328189501440)))
self.assertTrue(pl == (x - Integer(119538120)) * pl1)
x = var("x")
f20_1 = N20.eigenform_with_eigenvalue_t2(alpha20_1)
f20_2 = N20.eigenform_with_eigenvalue_t2(alpha20_2)
f20_3 = N20.eigenform_with_eigenvalue_t2(alpha20_3)
l = [f20_1, f20_2, f20_3]
l = [f.normalize(f[(1, 1, 1)]) for f in l]
cons20[-1] = coerce_pol(cons20[-1], alpha20_3.parent())
self.assertTrue(cons20 == [f._construction for f in l])
self.assertTrue(all(polynomial_to_form(c, 4) == f
for c, f in zip(cons20, l)))
dcts = [f20_1_dct, f20_2_dct, f20_3_dct]
self.assertTrue(all(coerce_dict(d, f.base_ring) == f.fc_dct for d, f in zip(dcts, l)))
def save_load_basis(self, wt):
KS = KlingenEisensteinAndCuspForms(wt, 10)
basis = KS.basis()
KS.save_basis_as_binary("/tmp/basis_test.sobj")
KS = KlingenEisensteinAndCuspForms(wt, 10)
KS.load_basis_from("/tmp/basis_test.sobj")
lbasis = KS.basis()
dim = KS.dimension()
self.assertTrue(all([lbasis[i].fc_dct == basis[i].fc_dct
for i in range(dim)]))
def test_wt_47_eigen(self):
KS47 = KlingenEisensteinAndCuspForms(47)
lambda2 = (-ZZ(957874176) / ZZ(13) * a47 ** 2 - ZZ(818321817600) / ZZ(13) * a47 -
ZZ(34324755775488))
x47 = KS47.eigenform_with_eigenvalue_t2(lambda2)
x47 = x47.normalize(x47[(2, -1, 3)])
_const47 = coerce_pol(cons47[0], a47.parent())
self.assertTrue(_const47 == x47._construction)
self.assertTrue(polynomial_to_form(_const47, x47.prec) == x47)
_x47_fc_dct = coerce_dict(x47_fc_dct, a47.parent())
self.assertTrue(x47.fc_dct == _x47_fc_dct)
S47 = CuspFormsDegree2(47)
x47 = S47.eigenform_with_eigenvalue_t2(lambda2)
x47 = x47.normalize(x47[(2, -1, 3)])
self.assertTrue(_const47 == x47._construction)
self.assertTrue(x47.fc_dct == _x47_fc_dct)