Simple Fourier trace formulas of Cubic Level and Applications

Qinghua Pi, Yingnan Wang, Lei Zhang

Published 2019-06-14Version 1

With the method of the relative trace formula and the classification of simple supercuspidal representations, we establish a simple Petersson trace formula and a simple Kuznetsov trace formula for automorphic forms on $GL(2)$ of cubic level. As applications, we obtain a non-vanishing result for central $L$-values of holomorphic newforms and some Weyl's laws for Maass newforms.