The first practical calculations: congruences for Ramanujan's tau function mod 13

We will describe how we are implementing Edixhoven's method for computing polynomials for the mod l Galois representations associated to modular forms. The computations are done in MAGMA, using modular symbols and numerical analysis. Recently, we have computed such polynomials for the mod 13 representation associated to Delta, the discriminant modular form of weight 12. In that case, we work with the modular curve X_1(13), which is of genus 2, and the polynomials have degrees 14 and 168.