# Polynomials for projective representations of level one forms

# Polynomials for projective representations of level one forms

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.

*Keywords:*
modular forms, Galois representations, cusp forms, polynomials, Ramanujan's tau function, Lehmer, nonvanishing conjecture

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