  The ALICE experiment is dedicated to the study of the Quark-Gluon Plasma
(QGP), a state of matter where, due to high temperature and density, quarks and
gluons are deconfined. One of the probes studied to investigate this state of
matter is the production of charmonium states, such as the J/$\psi$ and the
$\psi$(2S). Indeed, the presence of the QGP is expected to modify the
charmonium production yields, due to a balance between the color screening of
the charm quark potential and a recombination mechanism. A suppression of the
production yields in heavy ion collisions with respect to pp collisions scaled
by the mean number of binary nucleon-nucleon collisions was observed by ALICE
in Pb-Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{ s_{NN}}
= 2.76$ TeV. The observed suppression is smaller than the one found by PHENIX
at an order of magnitude lower collision energy. This behavior can be explained
by a stronger contribution from recombination processes at LHC than at lower
energies. In this presentation, we report on new results for the charmonium
production in Pb-Pb collisions measured at forward rapidity with the the muon
spectrometer of ALICE at $\sqrt{ s_{NN}} =5.02$ TeV and their comparison with
previous results and model predictions.
