  There are a number of fundamental results in the study of holomorphic
function theory associated to the discrete group PSL(2,Z) including the
following statements: The ring of holomorphic modular forms is generated by the
holomorphic Eisenstein series of weight four and six; the smallest weight cusp
form Delta has weight twelve and can be written as a polynomial in E4 and E6;
and the Hauptmodul j can be written as a multiple of E4 cubed divided by Delta.
The goal of the present article is to seek generalizations of these results to
some other genus zero arithmetic groups, namely those generated by Atkin-Lehner
involutions of level N with square-free level N.
