  We study the central charges and levels of 2d $\mathcal{N}=(0,4)$
superconformal field theories that are dual to four- and five-dimensional BPS
black holes in compactifications of type IIB string theory on a K3 surface.
They arise from wrapping a D3-brane on a curve $C$ inside K3 and have
transverse space either an ALE or ALF space. These D3-branes have an AdS$_3
\times \mathrm{S}^3/ \Gamma$ near horizon geometry where $\Gamma$ is a discrete
subgroup of $SU(2)$. We compute the central charges and levels of the 2d SCFTs
both in the microscopic picture and from six-dimensional $\mathcal{N}=(2,0)$
supergravity. These quantities determine the black hole entropy via Cardy's
formula. We find agreement between the microscopic and macroscopic
computations. The contributions from one-loop quantum corrections to the
macroscopic result are crucial for this matching.
