A radio-frequency filter with at least one dielectric multi-mode resonator is provided. The resonator includes a metal housing with a top surface, a bottom surface, four sectors between the top and bottom surfaces, and including a resonator cavity therein. The resonator further includes a dielectric body positioned inside the cavity, the dielectric body having a first thickness between the top and bottom surfaces of the cavity, wherein there is a gap between the sectors of the housing and the dielectric body, the dielectric body including a hollow on the surface facing the top surface of the housing and on the surface facing the bottom surface of the housing, the dielectric body thus having a second thickness at the location of the hollows, the second thickness being smaller than the first thickness.