When are the $l$-local $p$-adic Galois representations of Siegel modular forms semistable? By this I mean $\rho_{f}: G_{\mathbb{Q}}\to \operatorname{GSp}_{2n}(\overline{\mathbb{Q}}_p)$ restricted to the decomposition group at $l$. Is this controlled by the level? I am primarily interested in this when $l=p$ and $n=2$.