We describe an algorithm for decomposing certain modules attached to real nilpotent orbits into their irreducible components. These modules are prehomogeneous spaces in the sense of Sato and Kimura and arise in the study of nilpotent orbits and the representation theory of Lie groups. The output is a set of LATEX statements that can be compiled in a LATEX environment in order to produce tables. Although the algorithm is used to solve the problem in the case of exceptional real reductive Lie groups of inner type it does describe these spaces for the classical cases of inner type also. Complete tables for the exceptional groups can be found at http://www.math.umb.edu/~anoel/publications/tables/.