Klingen Vectors for Depth Zero Supercuspidals of $GSp(4)$

Let $F$ be a non-archimedean local field of characteristic zero and $(\pi ,V)$ a depth zero, irreducible, supercuspidal representation of $GSp(4,F)$. We calculate the dimensions of the spaces of Klingen-invariant vectors in $V$ of level ${\mathfrak{p}}^n$ for all $n\ge 0$.