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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 $N$ a prime.

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# SL(2,Z/N)-decomposition of space of cusp forms for Gamma(N)

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.