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In fact there is a "ready to use" procedure. M = ModularSymbols(N,2) creates the space of weight 2 modular symbols for $\Gamma_0(N)$ (i.e. a basis of $H^1(X_0(N), \mathbb{Z})$). We can create the element { $\alpha, \beta$ }, of M by putting x=M.modular_symbol([alpha, beta]). The n-th Hecke operator is computed as follow: M.T(n)(x)