  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.
