# Analogous theorem for Hilbert modular forms

I have studied modular forms and saw a correspondence like a newform correspond to a automorphic representation of $$\mathrm{GL}_n(\mathbb{A_Q})$$. Does any similar result holds for Hilbert modular forms?

Also we know $$S_k(\Gamma_1(M))= \bigoplus\nolimits_{\epsilon:(\mathbb{Z}/n\mathbb{Z})^*\to\mathbb{C}^*} S_k(\Gamma_0(M),\epsilon)$$ and $$\dim_{\mathbb{C}}S_k(\Gamma_1(M))$$ ~ $$M^2$$ where $$\Gamma_1(M)$$ and $$\Gamma_0(M)$$ are well-known congruence subgroups of $$\mathrm{SL}_2(\mathbb{Z})$$. $$S_k(\Gamma_1(M))$$ is the subspace of holomorphic cusp forms and $$S_k(\Gamma_0(M),\mathbb{\epsilon})$$ is the subspace of holomorphic cusp forms having character $$\epsilon$$. I want to know again if there are similar results for Hilbert modular forms or Hilbert Cusp forms.

If yes, please suggest some good references for this.