  We investigate the low-lying excitations of a weakly-interacting,
harmonically-trapped Bose-Einstein condensed gas under rotation, in the limit
where the angular mometum $L$ of the system is much less than the number of the
atoms $N$ in the trap. We show that in the asymptotic limit $N \to \infty$ the
excitation energy, measured from the energy of the lowest state, is given by
$27 N_{3}(N_{3}-1) v_0 /68$, where $N_{3}$ is the number of octupole
excitations and $v_{0}$ is the unit of the interaction energy.
