I was reading adelization of classical automorphic forms and learnt that each cusp form corresponds to a automorphic representation of $\operatorname{GL}_n(\mathbb{A}_\mathbb{Q})$. I understood the proof. But then I found a statement like that there is a one-to-one correspondance between newforms of the congruence subgroup $\Gamma_1(N)$ and the irreducible cuspidal representations of $\operatorname{GL}_n(\mathbb{A}_\mathbb{Q})$.

But I couldn't find any proof of it.
Please suggest some references.

Thank you.