A filter element has a holder arrangement with a filter bellows and a partition element arranged at different regions of the holder arrangement. The partition element extends between first and second chambers of a resonator structure when installed in a filter system and has a passage acoustically coupling the two chambers. Such a filter element is exchangeably arranged in the filter housing of the filter system which has a main inlet, a main outlet, and an auxiliary connection outlet. The filter bellows is arranged in flow direction between the main inlet and the two outlets. The partition element is arranged between the two chambers of the resonator structure for noise damping of the auxiliary connection outlet. Its passage acoustically couples the two chambers. The partition element projects into an auxiliary connection resonator region of the filter housing and has end regions contacting walls delimiting the auxiliary connection resonator region.