Polynomials for projective representations of level one forms

Abstract

This chapter explicitly computes mod-ℓ Galois representations attached to modular forms. To be precise, it looks at cases with l ≤ 23, and the modular forms considered will be cusp forms of level 1 and weight up to 22. The chapter presents the result in terms of polynomials associated with the projectivized representations. As an application, it will improve a known result on Lehmer's nonvanishing conjecture for Ramanujan's tau function.