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When does the double coset representative for a congruence subgroup contain a $\text{SL}_2(\mathbb{Z})$-conjugacy class?
In the paper p-adic L-functions and p-adic periods of modular forms, Greenberg/Stevens assert that if $\sigma_l:=\begin{pmatrix}l&0\\0&1\end{pmatrix}$ is the usual Hecke operator at $l$ double ...
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