In its simplest form the Petersson trace formula is as follows. Let be an orthonormal basis of , the space of cusp forms of weight on . Then for any positive integers we have
"Petersson and Kuznetsov trace formulas". Lie Groups and Automorphic Forms. AMS/IP Studies in Advanced Mathematics. Vol. 37. 2006. pp. 147–168. doi:10.1090/amsip/037/04. ISBN9780821841983.