Since $\Gamma(N)$ is normal in $\mathrm{SL}(2,\mathbb{Z})$, the quotient group $\mathrm{SL}(2,\mathbb{Z}/N)$ acts on the spaces of cusp forms $S\_k(\Gamma(N))$. How do these spaces decompose into irreducible representations? 


I can do the case $N=2$. I'm mostly interested in the case of $N$ a prime.



SL(2,Z/N)-decomposition of space of cusp forms for Gamma(N)
See Theorem 1.0.3 of Jared Weinstein's [phd thesis](http://www.math.ucla.edu/~jared/jswthesis.pdf) (it uses equivariant Riemann Roch). 


