  We introduce a simple method to extract the representation content of the
spectrum of a system with SU(2) symmetry from its partition function. The
method is easily generalized to systems with SO(2,4) symmetry, such as
conformal field theories in four dimensions. As a specific application we
obtain an explicit generating function for the representation content of free
planar Yang-Mills theory on S^3. The extension to N = 4 super Yang-Mills is
also discussed.
