Eta quotients (awaiting review)

An eta quotient is any function $f$ of the form \[ f(z)=\prod_{1\leq i\leq s}\eta^{r_i}(m_iz), \] where $m_i\in\mathbb{N}$ and $r_i\in\mathbb{Z}$ and $\eta(z)$ is the Dedekind eta function.

An eta product is an eta quotient in which all the $r_i$ are non-negative.