Let $\pi$ be an automorphic subrepresentation of a reductive group $G$. Here by this, I mean an irreducible representation realized in a subspace of the space of automorphic forms on $G$.
Let $m_\pi$ be the multiplicity of $\pi$ in the space of automorphic forms. Is it in general true that $m_\pi<\infty$? Of course, this is true if $\pi$ is cuspidal or residual. But I would like to know if it is true in general. Also I would like to know where the proof is written even for the cuspidal or residual case.