  An eta-quotient of level $N$ is a modular form of the shape $f(z) =
\prod_{\delta | N} \eta(\delta z)^{r_{\delta}}$. We study the problem of
determining levels $N$ for which the graded ring of holomorphic modular forms
for $\Gamma_{0}(N)$ is generated by (holomorphic, respectively weakly
holomorphic) eta-quotients of level $N$. In addition, we prove that if $f(z)$
is a holomorphic modular form that is non-vanishing on the upper half plane and
has integer Fourier coefficients at infinity, then $f(z)$ is an integer
multiple of an eta-quotient. Finally, we use our results to determine the
structure of the cuspidal subgroup of $J_{0}(2^{k})(\mathbb{Q})$.
