Given
$$ \left(\frac{\eta(5\tau)}{\eta(\tau)}\right)^{6}\;\; =\;\; \frac{r^5}{1-11r^5-r^{10}},\;\;\;\;\;\text{with}\;\;r\; =\; q^{1/5} \prod_{n=1}^\infty \frac{(1-q^{5n-1})(1-q^{5n-4})}{(1-q^{5n-2})(1-q^{5n-3})}$$
where $\eta(\tau)$ is the Dedekind eta function,
$$\eta(\tau) = q^{1/24} \prod_{n=1}^\infty (1-q^n)$$
and $q = \exp(2\pi i\tau)$, is there an analogous identity for,
$$ \left(\frac{\eta(13\tau)}{\eta(\tau)}\right)^{2}\;\; =\;\; ???$$