  We conjecture that the Fourier coefficients of a degree three Siegel form,
$1/\sqrt{\chi_{18}}$, count the degeneracy of three-center BPS bound states in
type II string theory compactified on $K3 \times T^2$. We provide evidence for
our conjecture in the form of consistency with physical considerations of
wall-crossing, holographic bounds, and the appearance of suitable counting
functions (involving the inverse of the modular discriminant $\Delta$ and the
inverse of the Igusa cusp form $\Phi_{10}$) in limits where the count
degenerates to involve single-center or two-center objects.
