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We outline an algorithm for computing Hecke operators on equivariantcohomology $H^\ast_{\Gamma_{\text{Sp}}}(X_{\text{Sp}};\rho)$ for the symplecticgroup $\text{Sp}_4(\mathbb{R})$. To do this, we define a new acyclic cellcomplex for $\text{Sp}_4(\mathbb{R})$ and make use of the well-temperedcomplex.

Computing Hecke operators for arithmetic subgroups of $\text{Sp}_4$