  We show that a dilute harmonically trapped two-component gas of fermionic
atoms with a weak repulsive interaction has a pronounced super-shell structure:
the shell fillings due to the spherical harmonic trapping potential are
modulated by a beat mode. This changes the ``magic numbers'' occurring between
the beat nodes by half a period. The length and amplitude of this beating mode
depend on the strength of the interaction. We give a simple interpretation of
the beat structure in terms of a semiclassical trace formula for the symmetry
breaking U(3) --> SO(3).
