Analytic evaluation of Hecke eigenvalues for classical modular forms

D. Armendariz, O. Colman, N. Coloma, A. Ghitza, N. Ryan, D. Teran
We propose a method for computing approximations to the Hecke eigenvalues of a classical modular eigenform f, based on the analytic evaluation of f at points in the upper half plane. Our approach works with arbitrary precision, allows for a strict control of the error in the approximation, and outperforms current exact computation methods.