Computing modular Galois representations for small $\ell$

Abstract

In this paper we describe an algorithm for computing mod $\ell$ Galois representations associated to modular forms of weight $k$ when $\ell <k-1$. As applications, we use this algorithm to explicitly compute the cases with ${\Delta }_k$ for $k=16,20,22,26$ and all the unexceptional primes $\ell$ with $\ell <k-1$.