CoCalc
Sharedsupport / 2016-02-14-modp-modform.sagewsOpen in CoCalc

Examples for support purposes...

def modp_reductions(f, p, prec=None):
    K = f.base_ring()
    g = f.q_expansion(prec)
    return [g.change_ring(P.residue_field()) for P, e in K.factor(p)]
f = CuspForms(23).newforms('a')[0]

modp_reductions(f, 5)
modp_reductions(f, 7)
modp_reductions(f, 11)
[q + 2*q^2 + 2*q^4 + 4*q^5 + O(q^6)] [q + a0bar*q^2 + (5*a0bar + 6)*q^3 + (6*a0bar + 6)*q^4 + 2*a0bar*q^5 + O(q^6)] [q + 7*q^2 + 7*q^3 + 3*q^4 + 3*q^5 + O(q^6), q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + O(q^6)]