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()))