Cs$_3$C$_{60}$ in the A15 structure is an antiferromagnet at ambient pressure in contrast with other superconducting trivalent fullerides. Superconductivity is recovered under pressure and reaches the highest critical temperature of the family. Comparing density-functional calculations with generalized gradient approximation to the hybrid functional HSE, which includes a suitable component of exchange, we establish that the antiferromagnetic state of Cs$_3$C$_{60}$ is not due to a Slater mechanism, and it is stabilized by electron correlation. HSE also reproduces the pressure-driven metalization. Our findings corroborate previous analyses suggesting that the properties of this compound can be understood as the result of the interplay between electron correlations and Jahn-Teller electron-phonon interaction.
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