  We report on cotunneling spectroscopy magnetoconductance measurements of
multi-hole ultraclean carbon nanotube quantum dots in the SU(4) Kondo regime
with strong spin-orbit coupling. Successive shells show a gradual weakening of
the Kondo effect with respect to the spin-orbital splittings, leading to an
evolution from SU(4) to SU(2) symmetry with a suppressed conductance at half
shell filling. The extracted energy level spectrum, overally consistent with
negligible disorder in the nanotube, shows in the half filled case large
renormalizations due to Coulombian effects.
