Hidden Symmetries and j(\tau)

Abstract

We show that for supersingular prime p the image of a unique meromorphic function G_p on X_0(p) (of degree two, with polar divisor {[0]_0,[\infty]_0}) under a certain Hecke operator is equal to j(\tau) (up to some additional constant). This generates quantities of relations between the coefficients of j(t) and leads to some group of hidden symmetries whose order must be divided by p.