We study the resonances of a forced turbulent wake past a flat-based bluffbody using symmetric and antisymmetric actuation modes. The natural, unforced wake flow exhibits broadband dynamics superimposed on oscillatory motions linked to the reminiscent laminar Bénard-von Kármán instability in the turbulent flow. Harmonic and subharmonic resonances can be controlled by the phase relationship of periodic forcing and are linked to the symmetry properties of vortex shedding. Symmetric forcing leads to a strong subharmonic amplification of vortex shedding in the wake, but no harmonic excitation. The robustness of the subharmonic resonance is confirmed at different Reynolds numbers. Antisymmetric actuation, however, promotes a harmonic resonance with very similar wake and drag features.