Siegel Vectors for Nongeneric Depth Zero Supercuspidals of $GSp(4)$

Let $F$ be a non-archimedean local field of characteristic zero. If $F$ has even residual characteristic, we assume $F\mathrm{/}{\mathbb{Q}}_2$ is unramified. Let $V$ be a depth zero, irreducible, nongeneric supercuspidal representation of $GSp(4,F)$. We calculate the dimensions of the spaces of Siegel-invariant vectors in $V$ of level ${\mathfrak{p}}^n$ for all $n\ge 0$.