  The alkali-doped fulleride Cs$_{3}$C$_{60}$, crystallized in the space group
Fm$\overline 3$m or Pm$\overline 3$n, exhibits unconventional $s$-wave
superconductivity under pressure with a maximum $T_c\sim 38$ K. Recently, a new
primitive-cubic-structured Cs$_{3}$C$_{60}$ phase corresponding to the space
group Pa$\overline 3$ has been reported (arXiv:2208.09429) and the authors
observed superconductivity at ambient pressure. Using density-functional theory
(DFT) calculations, we show that the proposed Pa$\overline 3$ structure is not
stable under ionic relaxation, but transforms into the FCC structure. We study
the normal and superconducting state of the stable FCC phase at different
temperatures and volumes using DFT plus dynamical mean-field theory (DFT+DMFT)
in the Nambu formalism. As temperature increases, the transition between
superconductor and normal metal (Mott insulator) at small (big) volume is found
to be second (first) order. The recently developed maximum entropy analytic
continuation method for the anomalous-self-energy is used to study the
momentum-resolved spectra and optical conductivity.
