(Sorry for poor my english skill..)

Let $k$ and $N$ be positive integers and $\chi$ be a Dirichlet character modulo $N$. Let $F$ be a newform with number field $K_{F}$. (All coefficients of $F$ in $K_{F}$.) Let $\ell$ be a prime and let $\lambda$ of $\mathcal{O}_{K_{F}}$ be a maximal ideal lying over $\ell$. By theorem 9.6.5 in "A first course in Modular forms - Diamond and Shurman", there is an irreducible 2-dimensional Galois representation \begin{equation} \rho_{F,\lambda} : G_{\mathbb{Q}} \to GL_2(K_{F,\lambda}). \end{equation} Someone told me that the conductor of $\rho_{F,\lambda}$ is same as the level of $F$ i.e. the conductor of $\rho_{F,\lambda}$ is $N$. Also he said that this fact is in the Carayol's paper, however I couldn't find it.

Is the fact true? If it is true, I would appreciate your reference.

Thanks for reading.