  Symplectic reflection algebra $ H_{1, \,\nu}(G)$ has a $T(G)$-dimensional
space of traces whereas, when considered as a superalgebra with a natural
parity, 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 on
the parameter $\nu$.
  In this paper, the values $T(G)$ and $S(G)$ are explicitly calculated for the
groups $G= \Gamma \wr S_N$, where $\Gamma$ is a finite subgroup of
$Sp(2,\mathbb C)$.
