Abstract

In this paper we list all the weight 2 newforms f(tau) that are products and quotients of the Dedekind eta-function eta(tau):=q(n=1)(1/24)Pi(infinity)(1-q(n)), where q := e(2 pi i tau). There are twelve such f(tau), and we give a model for the strong Well curve E whose Hasse-Weil L-function is the Mellin transform for each of them. Five of the f(tau) have complex multiplication, and we give elementary formulae for their Fourier coefficients which are sums of Hecke Grossencharacter values. These formulae follow easily from well known q-series infinite product identities.