I'm looking for a nice formula for a Hauptmodul for $\Gamma_1(3)$.
This is certainly very classical.A reference would be great.
2026-03-31 12:54:55.1774961695
Hauptmodul for $\Gamma_1(3)$
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The reference I found is the paper Modular Subgroups, Forms, Curves and Surfaces by Abdellah Sebbar. Table $3$ gives the Hauptmodul for $\Gamma(3)$, namely the modular form $$ \Big( \frac{\eta (\tau /3)}{\eta(3\tau)}\Big), $$ with the Dedekind eta funtion $\eta(z)$. The Hauptmodul for $\Gamma_1(3)$ is then the third power of the one of $\Gamma(3)$, if I understood this correctly.