  The elliptic modular j function enjoys many beautiful properties. Its Fourier
coefficients are related to the Monster group, and its CM values generate
abelian extensions over imaginary quadratic fields. Kaneko gave an arithmetic
formula for the Fourier coefficients expressed in terms of the traces of the CM
values. In this article, we are concerned with analogues of Kaneko's result for
the McKay-Thompson series of square-free level.
