  We study an Andreev quantum dot, that is a quantum dot inserted in a
superconducting ring, with several levels or conducting channels. We analyze
the degeneracy of the ground state as a function of the phase difference and of
the gate voltage and find its dependence on the Coulomb interaction within and
between channels. We compute a (non integer) charge of the dot region and
Josephson current. The charge-to-phase and current-to-gate voltage
sensitivities are studied. We find that, even in the presence of Coulomb
interaction between the channels, the sensitivity increases with the number of
channels, although it does not scale linearly as in the case with no
interactions. The Andreev quantum dot may therefore be used as a sensitive
detector of magnetic flux or as a Josephson transistor.
