Computing weight $2$ modular forms of level $p^2$

Abstract

For a prime p we describe an algorithm for computing the Brandt matrices giving the action of the Hecke operators on the space V of modular forms of weight 2 and level p 2 . For p ≡ 3 mod 4 we define a special Hecke stable subspace Vo of V which contains the space of modular forms with CM by the ring of integers of Q(√-p) and we describe the calculation of the corresponding Brandt matrices.