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Single centered supersymmetric black holes in four dimensions havespherically symmetric horizon and hence carry zero angular momentum. This leadsto a specific sign of the helicity trace index associated with these blackholes. Since the latter are given by the Fourier expansion coefficients ofappropriate meromorphic modular forms of Sp(2,Z) or its subgroup, we are led toa specific prediction for the signs of a subset of these Fourier coefficientswhich represent contributions from single centered black holes only. Weexplicitly test these predictions for the modular forms which compute the indexof quarter BPS black holes in heterotic string theory on T^6, as well as in Z_NCHL models for N=2,3,5,7.

How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?