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 $\ell <k-1$.