Modular Galois representations p-adically using Makdisi's moduli-friendly forms

We will present a p-adic method to compute Galois representations attached to modular forms. This method compares very favourably to the better-known complex-analytic approach. The main ingredient is the use of “moduli-friendly" forms introduced by Makdisi, which allow us to evaluate modular forms at p-adic points of modular curves, and thus to compute in the Jacobian of modular curves without writing down any equations nor q-expansions.