Self-dual representations of Sp(4,F)

Let $F$ be a non-Archimedean local field of characteristic $0$ and $G=Sp(4,F)$. Let $(\pi ,W)$ be an irreducible smooth self-dual representation $G$. The space $W$ of $\pi$ admits a non-degenerate $G$-invariant bilinear form $(,)$ which is unique up to scaling. The form $(,)$ is easily seen to be symmetric or skew-symmetric and we set $\epsilon (\pi )=\pm 1$ accordingly. In this paper, we show that $\epsilon (\pi )=1$ when $\pi$ is an Iwahori spherical representation of $G$.