Suppose $f$ is a weight $k$ cuspidal Hecke eigenform on the full modular group, with its L-function $L(s,f)$ normalized such that $s=1/2$ is the central point. Is a bound of the form

$\int_{-1}^{1}|L(1/2+it,f)|dt \gg_{\epsilon} k^{-\epsilon}$

known as $k\to \infty$? (Here as usual, $\epsilon>0$ is arbitrary.) I think I can do this myself, but I'd rather not if it's written somewhere...