Regularized inner products and weakly holomorphic Hecke eigenforms

Abstract

An interpretation of Guerzhoy's integral weight weakly holomorphic Hecke eigenforms via regularized inner products is given in this paper. In particular, Guerzhoy's eigenforms are eigenvectors in the quotient space of weakly holomorphic modular forms modulo a certain subspace, and it is shown in this paper that the subspace which is factored out is precisely the subspace that is orthogonal to all weakly holomorphic modular forms under an appropriate (regularize) inner product.postprin