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)})