The functions NewSubspace and NewformDecomposition may be applied to spaces of Bianchi modular forms. (See Chapter HILBERT MODULAR FORMS.)
> _<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]Since this cuspidal space has dimension 1, it consists of a single eigenform, whose eigenvalues can be read from the Hecke matrices: [Next][Prev] [Right] [Left] [Up] [Index] [Root]