Products of Eisenstein series and Fourier expansions of modular forms at cusps

Martin Dickson, Michael Neururer

We show, for levels of the form $N=p^a{q}^b{N}^{\prime }$ with $N^{\prime }$ squarefree, that in weights $k\ge 4$ every cusp form $f\in {\mathcal{S}}_k(N)$ is a linear combination of products of ce…