  The SW(3/2,2) current algebras come in two discrete series indexed by central
charge, with the chiral algebra of a supersymmetric sigma model on a Spin}(7)
manifold as a special case. The unitary representations of these algebras were
classified by Gepner and Noyvert, and we use their results to perform an
analysis of null descendants and compute the characters for every
representation. We obtain threshold relations between the characters of
discrete representations and those with continuous conformal weights. Modular
transformations are discussed, and we show that the continuous characters can
be written as bilinear combinations of characters for consecutive minimal
models.
