This question is a variant of this one.

Let $f$ be as in the other question, but suppose that we look at the $\ell$-adic representiation attached to $f$: $$ \rho_f : G_{\mathbb Q} \to \operatorname{GL}_2(E), $$ where $E$ is a finite extension of $\mathbb Q_\ell$, with $\ell$ a prime that does not divide $N$. Let $p \neq \ell$ be another prime that does not divide $N$.

What can be said about $\rho_{f,p}$, the restriction of $\rho_f$ to a decomposition subgroup at $p$?