Let $f$ be a newform (normalized, cuspidal) of weight $k \ge 2$. Then for a prime $\ell$ there is an $\ell$-adic Galois representation associated to $f$. If $k=2$, this comes from an abelian variety, hence the local representation at $\ell \nmid N$ arises from an $\ell$-divisible group, or finite flat group scheme of order $\ell^2$ if we look at the mod $\ell$ reduction. My understanding is that this is true in the case $k>2$, but I'm having trouble seeing why or finding a reference. I understand the construction of the representation using $H^1_{\acute{e}t}(X,\mathrm{Sym}^{k-2}(R^1_{\acute{e}t}f_* \underline{\mathbb{Z}_\ell}))$.

The reason for this is to use Raynaud's results to get a good local picture of the mod $\ell$ representation at primes dividing $\ell$.

I imagine one could just use the crystalline property in p-adic Hodge theory, but I'd like to see it in the more elementary way (and I understand that better).