On the representations generated by Eisenstein series of weight [formula omitted

Abstract

We consider the Eisenstein series E(z,s;k,χ,N) of weight k=(n+3)/2, level N>1 and a Dirichlet character χ modulo N such that χ2=1. Shimura proved that E(z,k/2;k,χ,N) is a nearly holomorphic function. We prove that E(z,k/2;k,χ,N) generates an indecomposable reducible (g,K)-module of length 2. These are new examples of indecomposable reducible (g,K)-modules generated by nearly holomorphic modular forms.