The Bekenstein-Hawking entropy of 1/16-BPS AdS_5 black holes is captured by a superconformal index. Such indices exhibit SL(3,Z) modular properties, which are explicated in terms of ambiguities in the Heegaard splitting of an associated Hopf surface. We conjecture a "modular factorization" of superconformal indices of general N=1 gauge theories and provide evidence for this conjecture by studying the free chiral multiplet and SQED.