Computing modular Galois representations for small $\ell$

TL;DR

This paper presents an algorithm to compute mod  Galois representations linked to modular forms of weight k for small primes , enabling explicit calculations for specific cases and primes.

Contribution

The paper introduces a new algorithm for computing mod  Galois representations for modular forms with  < k-1, expanding computational capabilities.

Findings

Successfully computed cases for =16,20,22,26

Explicit calculations for all unexceptional primes  < k-1

Enhanced understanding of Galois representations in modular forms

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 $\ell <k-1$.