On the cuspidal modular forms for the Fuchsian groups of the first kind

In this paper we study the construction and non-vanishing of cuspidal modular forms of weight m >= 3 for arbitrary Fuchsian groups of the first kind. We give a spanning set for the space of cuspidal modular forms S(m)(Gamma) of weight m >= 3 in a uniform way which does not depend on the fact that Gamma has cusps or not. (C) 2010 Elsevier Inc. All rights reserved.