  The representations of various color Lie superalgebras by Hilbert series are
the main topic of this work. The Color Lie superalgebras appear in various
branches of mathematics (e.g., topology, algebraic groups, etc.). They are
generalized Lie superalgebras. A generating function known as the Hilbert
series of color Lie superalgebras which encodes crucial knowledge about the
superalgebras representation. In particular, it provides a way to count the
number of states in the a given degree. We present a dimension formula that
resembles Witt's formula for free color Lie superalgebras, and a specific class
of color Lie p-superalgebras.
