The nonlinear dynamics of an inviscid magnetohydrodynamic system in a low-beta plasma is investigated through a simplified model obtained by a Galerkin projection. We show that a single Fourier mode dominates over the whole energy spectrum, a self-organization mechanism of turbulence being responsible for this nonlinear effect. Our results are in agreement with observations of an analogous phenomenon, say, the emergence of a quasi-single-helicity state both in numerical simulations and real experiments in reversed field pinch laboratory plasmas.