MAGMA Computational Algebra System

Newforms

The functions NewSubspace and NewformDecomposition may be applied to spaces of Bianchi modular forms. (See Chapter HILBERT MODULAR FORMS.)

Example ModFrmBianchi_hecke (H127E2)

> _<x> := PolynomialRing(Rationals());
>  F := NumberField(x^2+14);
>  OF := Integers(F);
>  level := (Factorization(3*OF)[1][1])^2;
>  M9 := BianchiCuspForms(F, level);
>  P:=Factorization(23*OF);
>  P[1,1];
Prime Ideal of OF
Two element generators:
    [23, 0]
    [3, 1]
>  HeckeOperator(M9, P[1,1]);
[8]
>  P[2,1];
Prime Ideal of OF
Two element generators:
    [23, 0]
    [20, 1]
>  HeckeOperator(M9, P[2,1]);
[-8]
>  HeckeOperator(M9, 2*OF);
[1]