Explicit formulae for linear characters of ${\Gamma }_0(N)$

Abstract

We give explicit formulae for a class of complex linear unitary characters of the congruence subgroups ${\Gamma }_0(N)$ which involve a variant of Rademacher's $\Psi$ function. We then prove that these characters cover all characters of ${\Gamma }_0(N)$ precisely when $N=1,2,3,4,5,6,7,8,10,12,13$.

15 pages; published in Communications in Algebra

References in corpus (1)

• Double coset operators and eta-quotients