Ionospheric feedback instability generates field line eigenmodes under favorable conditions of low ionospheric conductivity and high electric convection. A numerical study has been performed using a two-dimensional model in dipole magnetic field geometry that includes active ionospheric feedback and shear Alfv¿n wave dynamics of the magnetospheric response. Strong parallel inhomogeneities of the magnetospheric parameters included in the numerical model permit the simultaneous development of local ionospheric resonator modes (fast feedback) trapped between the ionosphere and Alfv¿n speed maximum above it and field line eigenmodes (slow feedback) that stand along the entire magnetic field line between two conjugate ionospheres. Fourier analysis of the numerical solution has been used to investigate the relative contribution of fast and slow feedback in the global dynamics of magnetosphere--ionosphere coupling. While many harmonics of the global magnetospheric resonator can be simultaneously generated by the ionospheric feedback instability, all modes above the fundamental eigenmode are strongly suppressed by Alfv¿n wave dispersion. The numerical results suggest that ionospheric feedback is a generating mechanism for the formation of narrow field line resonances.