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Symplectic reflection algebra $ H_{1, \,\nu}(G)$ has a $T(G)$-dimensionalspace of traces whereas, when considered as a superalgebra with a naturalparity, it has an $S(G)$-dimensional space of supertraces. The values of $T(G)$and $S(G)$ depend on the symplectic reflection group $G$ and do not depend onthe parameter $\nu$.  In this paper, the values $T(G)$ and $S(G)$ are explicitly calculated for thegroups $G= \Gamma \wr S_N$, where $\Gamma$ is a finite subgroup of$Sp(2,\mathbb C)$.

The number of independent Traces and Supertraces on the Symplectic Reflection Algebra $H_{1,\nu}(\Gamma \wr S_N)$