def test_det_is_divisible_x35_fifth():
prec = 18
x35 = x35_with_prec(prec)
f187 = ModFormQexpLevel1.load_from(os.path.join(data_dir,
"gens_even_det.sobj"))
es4 = eisenstein_series_degree2(4, prec)
es6 = eisenstein_series_degree2(6, prec)
g = (x35 ** 5) * (es4 ** 3 - es6 ** 2)
assert f187 * g[(16, 5, 10)] == g * f187[(16, 5, 10)]
def polynomial_to_form(f, prec):
es4 = eisenstein_series_degree2(4, prec)
es6 = eisenstein_series_degree2(6, prec)
x10 = x10_with_prec(prec)
x12 = x12_with_prec(prec)
x35 = x35_with_prec(prec)
gens = [es4, es6, x10, x12, x35]
def monom(t):
return reduce(operator.mul, [f ** a for f, a in zip(gens, t)])
return sum([a * monom(t) for t, a in f.dict().iteritems()])
def test_wt_35_eigenvalues(self):
x35 = x35_with_prec([(12, 33, 27), (8, 35, 39), (34, -17, 51)])
d = {2: -25073418240,
3: -11824551571578840,
4: 138590166352717152256,
5: 9470081642319930937500,
7: -10370198954152041951342796400,
9: -96268467952179923650803475996239,
11: -8015071689632034858364818146947656,
13: -20232136256107650938383898249808243380,
17: 118646313906984767985086867381297558266980}
d1 = {m: x35.hecke_eigenvalue(m) for m in d.keys()}
self.assertTrue(d == d1)
def check_det_with_prec(prec):
es4 = eisenstein_series_degree2(4, prec)
es6 = eisenstein_series_degree2(6, prec)
x35 = x35_with_prec(prec)
f = (es4**3 - es6**2) * x35**6
t = f._none_zero_tpl()
d = calculator.forms_dict(prec)
# Constructions of the first 11 generators.
cs = list(sorted(calculator._const_vecs, key=lambda x: x.weight()))[:11]
wt = sum(c.weight() for c in cs) + (10 * 11)//2
mat = [d[c].forms for c in cs]
det = det_deg2(mat, wt=wt)
assert f[t] * det == det[t] * f
ff_qsrx10 = qsrx10.change_ring(ffld)
dzx10 = x10.differentiate_wrt_z()
ff_dzx10 = dzx10.change_ring(ffld)
x12 = x12_with_prec(global_prec)
qsrx12 = QexpLevel1(x12.fc_dct, global_prec, is_cuspidal=True,
base_ring=ZZ)
dzx12 = x12.differentiate_wrt_z()
ff_x12 = x12.change_ring(ffld)
ff_qsrx12 = qsrx12.change_ring(ffld)
ff_dzx12 = dzx12.change_ring(ffld)
x35 = x35_with_prec(global_prec)
ff_x35 = x35.change_ring(ffld)
dct_of_forms = {"es4": es4,
"qsres4": qsres4,
"es6": es6,
"qsres6": qsres6,
"x10": x10,
"qsrx10": qsrx10,
"x12": x12,
"qsrx12": qsrx12,
"dzx10": dzx10,
"dzx12": dzx12,
"x35": x35,
"2": 2,
"0": 0,
def test_x35(self):
x35 = x35_with_prec(global_prec)
self.assertTrue(self.sub_dct(x35) == fc_dct35)
