The 3rd root of the modular invariant $j$ is
$$ j(\tau)^{1/3}=1+ 248q+ 4124q^2+ 34752q^3+\cdots,$$
where $q=e^{2\pi i \tau}$.

I was wondering if $j(\tau)^{1/3}$ the hauptmodul for the congruence subgroup generated by $\tau \rightarrow \tau+3, \tau \rightarrow-1/\tau$.

Thanks a lot!