The Modular Degree and the Congruence Number of a Weight 2 Cusp Form

Abstract

Let f be a weight 2 normalized newform on the congruence subgroup Γ0(N) with integral Fourier coefficients. There are two important numerical invariants attached to f : its congruence number and its modular degree. By definition, the congruence number of f is the largest integer Df such that there exists a weight 2 cusp form on Γ0(N), with integral… (More)

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