A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup Γ 0 (2) of the modular group SL 2 (Z) is constructed. These nonlinear equations are analogues of the well known Ramanujan equations, as well as the Chazy and Darboux-Halphen equations associated with the modular group. The general solutions of these equations can be realized in terms of the Schwarz triangle function S(0, 0, 1/2; z).