Proof: BoolElt                      Default: true

    Proof: BoolElt                      Default: true

Example ModSS_Associated (H144E5)

We compute the Brandt module and modular symbols spaces associated to the supersingular module for p=3, N=11, and verify that T₂ has the same characteristic polynomial on each.

> M := SupersingularModule(3,11);
> B := BrandtModule(M); B;
Brandt module of level (3,11), dimension 2, and degree 2 over
Integer Ring
> MS := ModularSymbols(M); MS;
Modular symbols space for Gamma_0(33) of weight 2 and dimension 4
over Rational Field
> Factorization(CharacteristicPolynomial(HeckeOperator(B, 2)));
[
    <$.1 - 3, 1>,
    <$.1 - 1, 1>
]
> Factorization(CharacteristicPolynomial(HeckeOperator(MS, 2)));
[
    <$.1 - 3, 2>,
    <$.1 - 1, 2>
]

There is an associated Brandt module even if the underlying computations on M are done using the Mestre-Oesterle graph method.

> M := SupersingularModule(11);
> UsesMestre(M);
true
> B := BrandtModule(M); B;   // takes a while
Brandt module of level (11,1), dimension 2, and degree 2 over
Integer Ring