On Fourier Coefficients of Modular Forms

Abstract

In this paper we generalize these results and find recursive formulae for the Fourier coefficients of any meromorphic modular form f on any genuszero group commensurable with SL(2, Z), including noncongruence groups and expansions at irregular cusps. The form of the recurrence relations is well suited for the computation of the Fourier coefficients of the functions and forms on the groups which occur in monstrous and generalized moonshine. The required initial data has, in many cases, been computed by Norton (private communication).2010 Mathematics subject classification: primary 11F30; secondary 11F12, 11F03.