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The Brandt module associated to M.
Proof: BoolElt Default: true
The space of modular symbols corresponding to M.
Proof: BoolElt Default: true
The +1 or -1 quotient of the space of modular symbols
corresponding to M.
The Z-module V underlying M along with an invertible map
V -> M.
We compute the Brandt module and modular symbols spaces associated
to the supersingular module for p=3, N=11, and verify that T_2
acts in a compatible way on them.
> 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 of level 33, weight 2, and dimension 4
> Factorization(CharacteristicPolynomial(HeckeOperator(B,2)));
[
<.1 - 3, 1>,
<.1 - 1, 1>
]
> Factorization(CharacteristicPolynomial(HeckeOperator(MS,2)));
[
<.1 - 3, 2>,
<.1 - 1, 2>
]
The Brandt module is defined 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
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