The Kolmogorov flow generated by a stationary one-dimensional forcing varying sinusoidally in space is studied using direct numerical simulations with periodic boundary conditions. The velocity statistics are considered for various computational domains ranging from the minimal cubic box with size equal to the forcing wavelength to significantly larger domains. For the minimal computational domain, the velocity statistics exhibit symmetries that are directly imposed by the forcing properties. However, for larger domains, the translational invariance in the streamwise direction appears to be broken and the turbulence statistics depend on the computational box aspect ratio.