189-726B: Modular Forms II Assignment 3

Due: Wednesday, January 30

1. Let f = ∑_{n} a_{n}q^{n} be a cusp form of weight 2 on Γ_{0}(N). How many fourier coefficients of f would you need to know in order to evaluate L(f, 1) with a numerical error of at most ϵ > 0? (Give your answer as a function of N and ϵ.) Same question for L(f, χ, 1) (where your answer will now depend on N, the conductor m of χ, and ϵ.)