  We derive the general anomaly polynomial for a class of two-dimensional CFTs
arising as twisted compactifications of a higher-dimensional theory on compact
manifolds $\mathcal{M}_d$, including the contribution of the isometries of
$\mathcal{M}_d$. We then use the result to perform a counting of microstates
for electrically charged and rotating supersymmetric black strings in
AdS$_5\times S^5$ and AdS$_7\times S^4$ with horizon topology BTZ$ \ltimes S^2$
and BTZ$ \ltimes S^2 \times \Sigma_\mathfrak{g}$, respectively, where
$\Sigma_\mathfrak{g}$ is a Riemann surface. We explicitly construct the latter
class of solutions by uplifting a class of four-dimensional rotating black
holes. We provide a microscopic explanation of the entropy of such black holes
by using a charged version of the Cardy formula.
