Definition of Automorphic Representation

Question

I would like to think of an automorphic representation as a representation weakly contained in $L^2(G_F\backslash G_A)$ where $G_A$ is the reductive group of rational points in the adeles over $F$, $F$ a number field. I know there is other definitions, I just want to know if this is correct. A representation is automorphic iff is weakly contained in $L^2(G_F\backslash G_A)$. There are references that suggest this but none of them officially makes the claim. A reference that makes this claim explicit will be much appreciated.