On the coefficients of certain modular forms belonging to subgroups of the modular group

Abstract

1. Introducton. The Fourier coefficients of modular forms F(r) of positive dimension have been determinedt for the case in which F(Q) belongs to the full modular group. It is the purpose of this paper to generalize some of those results to the case where F(r) belongs to an arbitrary subgroup of the modular group subject to certain restrictions. By F(r) belonging to a subgroup 7y we mean that F(r) is analytic in the upper half-plane I((r) >0 and that F(r) satisfies a transformation equation