Hecke groups H(Z) are the discrete subgroups of PSL(2, R) (the group of orientation preserving isometries of the upper half plane U) generated by two linear fractional transformations R (z) == - 1 / z and T (z) = z + X where XeR, X > 2 or X = Xq = 2cos (tt j q), qeN, q > 3^. These values of X are the only ones that give discrete groups, by a theorem of E. Hecke. We are going to be interested in the latter case /. = The element S = RT is then elliptic of order q. It is well-known that H (Xq) is the free product of two cyclic groups of orders 2 and q, i.e. H (Xq) S C2 * so that the signature of H (Zq) is (O; 2, q, oo).