Example ModFrmBianchi_creation-example (H150E1)

We create spaces of modular forms over Q(Sqrt( - 14)) for various levels.

> _<x> := PolynomialRing(Rationals());
> F := NumberField(x^2 + 14);
> OF := Integers(F);
> level := 1*OF;
> M := BianchiCuspForms(F, level);
> M;
Cuspidal space of Bianchi modular forms over
    Number Field with defining polynomial x^2 + 14 over the Rational Field 
    Level = Ideal of norm 1 generated by ( [1, 0] )
    Weight = 2
>  time Dimension(M);
0
Time: 0.050

We now define a space with level equal to the square of one of the split primes dividing 3.

> level := (Factorization(3*OF)[1][1])^2;
> Norm(level);
9
> time M9 := BianchiCuspForms(F, level);
Time: 1.370
> time Dimension(M9);
1
Time: 0.370

When defining this space, we may tell Magma to use the same Voronoi data, to avoid repeating this expensive precomputation:

> time M9 := BianchiCuspForms(F, level : VorData := VoronoiData(M) );
Time: 0.000
> time Dimension(M9);
1
Time: 0.370
> M9;
Cuspidal space of Bianchi modular forms over
    Number Field with defining polynomial z^2 + 14 over the Rational Field 
    Level = Ideal of norm 9 generated by ( [9, 0], [5, 2] )
    Weight = 2
    Dimension 1

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