def save_sym8_odd_form(key, prec=sym8_odd_prec): fname = fname_sym8_odd(key, prec) if os.path.exists(fname): return None es4, es6, x10, x12, x35 = degree2_modular_forms_ring_level1_gens(prec) if key in sym8_odd_dct: wt_dcts = sym8_odd_dct[key] gens_dct = {4: es4, 6: es6, 10: x10, 12: x12, 35: x35} fs = [mul([gens_dct[k]**i for k, i in d.items()]) for d in wt_dcts] f = rankin_cohen_triple_det_sym8(*fs) elif key == "h15": f10 = rankin_cohen_pair_x5(_rankin_cohen_pair_sym_pol(8, 5, 5), prec) f = vector_valued_rankin_cohen(es4, f10) elif key == "h17": f12 = rankin_cohen_pair_det2_sym(8, es4, es6) f = vector_valued_rankin_cohen(es4, f12) f.save_as_binary(fname)
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 rankin_cohen_quadruple_det3_sym_1(j, f1, f2, f3, f4): """ Returns a modular form of wt sym(j) det^(sum + 3). """ F = rankin_cohen_pair_det2_sym(j, f1, f2) * f3 return vector_valued_rankin_cohen(f4, F)