Computing modular Galois representations for small $\mathrm{\ell }$

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