On the automorphic forms of a noncongruence subgroup (Q1085196)

This paper gives the first example of a noncongruence subgroup which is ''essentially cuspidal'', that is, for which cuspidal eigenfunctions exist in abundance. It is a discrete subgroup of \(SL_ 2({\mathbb{C}})\) obtained as the kernel of a Kubota symbol. The proof consists of the explicit evaluation of the Eisenstein matrix associated to this subgroup, as well as its determinant. From these follows a Weyl law which gives the precise asymptotics of the cusp forms.