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