Consider a classical space $ M_k(N)$ of elliptic modular forms of weight $ k$ for $ \Gamma_0(N)$ . The definition of an unramified Hecke operator $ T_{p^m}$ in terms of double cosets is the disjoint union of double cosets $ $ \Gamma_0(N) \begin{pmatrix} a&b \ c&d \end{pmatrix} \Gamma_0(N),$ $ where $ a, b, c, dRead more