Class numbers and invariant characters of ${\mathfrak{sl}}_2({\mathbb{F}}_p)$

Zhe Chen, Yongqi Feng

Let $p$ be a prime and let $S_2(\Gamma (p))$ be the space of weight $2$ cusp forms for the principal congruence subgroup $\Gamma (p)$. Then ${\mathrm{SL}}_2({\mathbb{F}}_p)$ acts on $S_2(\Gamma (p))$ in…