We report on the characterization of near-ultraviolet high density silicon
photomultiplier (\SiPM) developed at Fondazione Bruno Kessler (\FBK) at
cryogenic temperature. A dedicated setup was built to measure the primary dark
noise and correlated noise of the \SiPMs\ between 40 and 300~K. Moreover, an
analysis program and data acquisition system were developed to allow the
precise characterization of these parameters, some of which can vary up to 7
orders of magnitude between room temperature and 40~K. We demonstrate that it
is possible to operate the \FBK\ near-ultraviolet high density \SiPMs\ at
temperatures lower than 100~K with a dark rate below 0.01 cps/mm2 and total
correlated noise probability below 35\% at an over-voltage of 6~V. These
results are relevant for the development of future cryogenic particle detectors
using \SiPMs\ as photosensors