  Recent progress in the understanding of the statistical nature of black hole
entropy shows that the counting functions in certain classes of models are
determined by automorphic forms of higher rank. In this paper we combine these
results with Langlands' reciprocity conjecture to view black holes as probes of
the geometry of spacetime. This point of view can be applied in any framework
leading to automorphic forms, independently of the degree of supersymmetry of
the models. In the present work we focus on the class of
Chaudhuri-Hockney-Lykken compactifications defined as quotients associated to
$\mathZ_N$ groups. We show that the black hole entropy of these CHL$_N$ models
can be derived from elliptic motives, thereby providing the simplest possible
geometric building blocks of the Siegel type entropy count.
