  We show that BPS jumping loci -- loci in the moduli space of string
compactifications where the number of BPS states jumps in an upper
semi-continuous manner -- naturally appear as Fourier coefficients of (vector
space-valued) automorphic forms. For the case of $T^2$ compactification, the
jumping loci are governed by a modular form studied by Hirzebruch and Zagier,
while the jumping loci in K3 compactification appear in a story developed by
Oda and Kudla-Millson in arithmetic geometry. We also comment on some curious
related automorphy in the physics of black hole attractors and flux vacua.
