Cuspidal projections of products of Eisenstein series (Q2071690)

Eisenstein series and their products generate the whole space of modular forms, but a product of Eisenstein series is not a cuspform. The paper studies whether the cuspidal projection of a product of Eisenstein Series is a cuspidal eigenform and gives complete solution of the cases when a product of two or three Eisenstein series of level one is taken. Namely, the product is not an eigenform when the dimension of the cuspidal subspace is \(>1\). The paper also studies special cases of the product of four and more Eisenstein series.