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)
