The Brandt module associated to the supersingular module M.
Proof: BoolElt Default: true
The space of modular symbols corresponding to the supersingular module M.
Proof: BoolElt Default: true
The +1 or -1 quotient of the space of modular symbols corresponding to the supersingular module M.
The Z-module V underlying the supersingular module M along with an invertible map V -> M.
> 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