  In this paper we will give necessary and sufficient conditions for the
operator $T_\nu^s$ to be in the symmetrically normed ideal $\mathcal{C}_\Phi$
for an arbitrary symmetric norming function $\Phi$ where $T_\nu$ is the
Toeplitz operator on the generalized Fock Space (also known as the generalized
Bargmann-Fock space) with a positive measure symbol $\nu$ and $0<s\leq 1$.
