  We show, for levels of the form $N = p^a q^b N'$ with $N'$ squarefree, that
in weights $k \geq 4$ every cusp form $f \in \mathcal{S}_k(N)$ is a linear
combination of products of certain Eisenstein series of lower weight. In weight
$k=2$ we show that the forms $f$ which can be obtained in this way are
precisely those in the subspace generated by eigenforms $g$ with $L(g, 1) \neq
0$. As an application of such representations of modular forms we can calculate
Fourier expansions of modular forms at arbitrary cusps and we give several
examples of such expansions in the last section.
