  We prove a Lindel\"of on average bound for the eighth moment of a family of
$L$-functions attached to automorphic forms on $GL(2)$, the first time this has
been accomplished. Previously, such a bound had been proven for the sixth
moment for our family by Djankovi\'c and for a similar family by Young. Our
proof rests on a new approach which overcomes the lack of perfect orthogonality
in the family initially observed by Iwaniec and Xiaoqing Li.
