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}))
