A Brandt module M is equipped with a family of linear Hecke operators which act on it. These are returned as matrices, which act on the right with respect to the basis Basis(M), but the Hecke operators of the ambient module may also be applied to elements of submodules. The system of Hecke operators are computed by default using the theta series which define the classical Brandt matrices. If a module is created with the ComputeGram parameter set to false, the Hecke operators are determined by means of enumeration of ideals in a p-neighbouring operation analogous to the method of graphs approach of Mestre and Oesterlé [Mes86].
Compute a matrix representing the nth Hecke operator Tn with respect to Basis(M) for the Brandt module M.
Computes the Atkin--Lehner operator on the Brandt module M, where p is a prime dividing the discriminant of M.