  Invariance under modular transformations and spectral flow restrict the
possible spectra of superconformal field theories (SCFT). This paper presents a
technique to calculate the number of constraints on the polar spectra of
N=(2,2) and N=(4,0) SCFT's by analyzing the elliptic genus. The polar spectrum
corresponds to the principal part of a Laurent expansion derived from the
elliptic genus. From the point of view of the AdS_3/CFT_2 correspondence, these
are the states which lie below the cosmic censorship bound in classical
gravity. The dimension of the space of elliptic genera is obtained as the
number of coefficients of the principal part minus the number of constraints.
As an additional illustration of the technique, the constraints on the spectrum
of N=4 topologically twisted Yang-Mills on CP^2 are discussed.
