A level N reduction theory of indefinite binary quadratic forms
  In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup \Gamma^0(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q_1, . . ., Q_n that this algorithm produces are such that the the corresponding paths \gamma_1, . . ., \gamma_n in the Riemann surface X0(N)(C) have a nice behavior around the elliptic points of order 2. 
Carlos Castano-Bernard