Black holes carry more information about the microstates than just the total degeneracy. As a concrete example, the N -twined helicity trace indices for 1 4 -BPS black holes of the CHL models allow extracting information about the distribution of the N charges among the black hole microstates. The number of black hole microstates carrying a definite eigenvalue under the generator of the N twining group must be positive. This leads to a specific prediction for the signs of certain linear combinations of Fourier coefficients of Siegel modular forms. We explicitly test these predictions for low charges. In the D1-D5-P duality frame, we compute the appropriate hair removed partition functions and show the positivity of the appropriate Fourier coefficients for low charges. We present various consistency checks on our computations.