  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
$\ell <k-1$.
