  We study the interplay between four-derivative 4d gauged supergravity,
holography, wrapped M5-branes, and theories of class $\mathcal{R}$. Using
results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d
correspondence we are able to constrain the two independent coefficients in the
four-derivative supergravity Lagrangian. This in turn allows us to calculate
the subleading terms in the large-$N$ expansion of supersymmetric partition
functions for an infinite class of three-dimensional $\mathcal{N}=2$ SCFTs of
class $\mathcal{R}$. We also determine the leading correction to the
Bekenstein-Hawking entropy of asymptotically AdS$_4$ black holes arising from
wrapped M5-branes. In addition, we propose and test some conjectures about the
perturbative partition function of Chern-Simons theory with complexified ADE
gauge groups on closed hyperbolic three-manifolds.
