def test_vector_valued_rankin_cohen(self):
prec = 5
M4_10 = vvld_smfs(4, 10, prec)
f4_10 = M4_10.basis()[0]
f4_15 = vvld_smfs(4, 15, prec).basis()[0]
e4 = eisenstein_series_degree2(4, prec)
g4_15 = vector_valued_rankin_cohen(e4, f4_10)
t = ((1, 1, 1), 0)
self.assertEqual(f4_15 * g4_15[t], g4_15 * f4_15[t])
es4, es6, _, _, _ = degree2_modular_forms_ring_level1_gens(5)
f = es6
x5 = x5__with_prec(5)
f_even_sym2 = rankin_cohen_pair_sym(2, f, x5)
f_odd_sym2 = vector_valued_rankin_cohen(es4 * x5, f_even_sym2)
a = f_odd_sym2[(1, 0, 2)].vec[1]
g_sym2_21 = vvld_smfs(2, 21, 4).basis()[0]
b = g_sym2_21[(1, 0, 2)].vec[1]
self.assertEqual(f_odd_sym2 * b, g_sym2_21 * a)
def test_vecor_valued_klingen(self):
lst = [(18, 2), (20, 2), (12, 4), (14, 4)]
R = PolynomialRing(QQ, names="x")
x = R.gens()[0]
def euler_factor_at_2(f):
wt = f.weight()
return 1 - f[2] * x + 2 ** (wt - 1) * x ** 2
for k, j in lst:
M = vvld_smfs(j, k, 4)
S = CuspForms(1, j + k)
f = S.basis()[0]
f = f * f[1] ** (-1)
pl = euler_factor_at_2(f)
lam = (1 + 2 ** (k - 2)) * f[2]
F = M.eigenform_with_eigenvalue_t2(lam)
self.assertEqual(R(F.euler_factor_of_spinor_l(2)),
pl * pl.subs({x: 2 ** (k - 2) * x}))
def test_vecor_valued_misc(self):
prec = 5
M = vvld_smfs(2, 20, prec)
m = matrix([M._to_vector(f).list() for f in M.basis()])
self.assertEqual(m, identity_matrix(QQ, M.dimension()))
