  Let $\Gamma$ be a non-uniform lattice in $SL(2, \mathbb R)$. In this paper,
we study various $L^2$-norms of automorphic representations of $SL(2, \mathbb
R)$. We bound these norms with intrinsic norms defined on the representation.
Comparison of these norms will help us understand the growth of $L$-functions
in a systematic way.
