def _hecke_pol_klingen(k, j):
'''k: even.
F: Kligen-Eisenstein series of determinant weight k whose Hecke field is
the rational filed. Return the Hecke polynomial of F at 2.
'''
f = CuspForms(1, k + j).basis()[0]
R = PolynomialRing(QQ, names="x")
x = R.gens()[0]
pl = QQ(1) - f[2] * x + QQ(2) ** (k + j - 1) * x ** 2
return pl * pl.subs({x: x * QQ(2) ** (k - 2)})
