We use deep $HST$ WFC3/IR imaging to study the Initial Mass Function (IMF) of the ultra faint dwarf galaxy Coma Berenices (Com Ber). Our observations reach the lowest stellar mass ever probed in a resolved galaxy, with 50% completeness at $sim 0.17$ M$_{odot}$. Unresolved background galaxies however limit our purity below $sim 0.23$ M$_{odot}$. If modeled with a single power law, we find that the IMF slope is $-1.45^{+0.29}_{-0.3}$ (68% credible intervals), compared to a Milky Way value of $-2.3$. For a broken power law, we obtain a low-mass slope of $-1.18_{-0.33}^{+0.49}$, a high-mass slope of $-1.88_{-0.49}^{+0.43}$ and a break mass of $0.57_{-0.08}^{+0.12}$ M$_{odot}$, compared to $-1.3$, $-2.3$ and 0.5 M$_{odot}$ for a Kroupa IMF. For a log-normal IMF model we obtain values of $0.33_{-0.16}^{+0.15}$ M$_{odot}$ for the location parameter and of $0.68_{-0.12}^{+0.17}$ for $sigma$ (0.22 M$_{odot}$ and 0.57 for the Chabrier system IMF). All three parametrizations produce similar agreement with the data. Our results agree with previous analysis of shallower optical HST data. However analysis of similar optical data of other dwarfs finds IMFs significantly more bottom-light than in the Milky Way. These results suggest two, non mutually exclusive, possibilities: that the discrepancy of the dwarf galaxies IMF with respect to the Milky Way is, at least partly, an artifact of using a single power law model, and that there is real variance in the IMF at low masses between the currently studied nearby dwarfs, with Com Ber being similar to the Milky Way, but other dwarfs differing significantly.
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