Let $k \geq 2$ and $N \geq 1$ be integers, let $\varepsilon : (\mathbb{Z}/N\mathbb{Z})^\times \to \mathbb{C}^\times$ be a Dirichlet character, and let $f \in S_k(\Gamma_1(N), \varepsilon)$ be a normalized cuspidal Hecke eigenform. Let $K_f$ be the number field generated by the Hecke eigenvalues of $f$. For every finite place $\lambda$ of $K_f$ lying above a rational prime $\ell$, let

\begin{align*} \rho_{f,\lambda}: G_{\mathbb{Q}} \to GL_2(K_{f,\lambda}) \end{align*}

be Deligne's $\lambda$-adic Galois representation attached to $f$. Then the restriction

\begin{align*} \rho_{f,\lambda}\big|_{G_{\mathbb{Q}_\ell}}: G_{\mathbb{Q}_\ell} \to GL_2(K_{f,\lambda}) \end{align*}

is Hodge-Tate. With the convention that the $\ell$-adic cyclotomic character has Hodge-Tate weight $1$, its Hodge-Tate weights, counted with multiplicity, are exactly

\begin{align*} \{0, k-1\}. \end{align*}