The very nearby Type Ia supernova 2014J in M82 offers a rare opportunity to study the physics of thermonuclear supernovae at extremely late phases ($gtrsim$800 days). Using the Hubble Space Telescope (HST), we obtained six epochs of high precision photometry for SN 2014J from 277 days to 1181 days past the $B-$band maximum light. The reprocessing of electrons and X-rays emitted by the radioactive decay chain $^{57}$Co$rightarrow ^{57}$Fe are needed to explain the significant flattening of both the $F606W$-band and the pseudo-bolometric light curves. The flattening confirms previous predictions that the late-time evolution of type Ia supernova luminosities requires additional energy input from the decay of $^{57}$Co (Seitenzahl et al. 2009). By assuming the $F606W$-band luminosity scales with the bolometric luminosity at $sim$500 days after the $B-$band maximum light, a mass ratio $^{57}$Ni/$^{56}$Ni$sim$0.065$_{-0.004}^{+0.005}$ is required. This mass ratio is roughly $sim$3 times the solar ratio and favors a progenitor white dwarf with a mass near the Chandrasekhar limit. A similar fit using the constructed pseudo-bolometric luminosity gives a mass ratio $^{57}$Ni/$^{56}$Ni$sim$0.066$_{-0.008}^{+0.009}$. Astrometric tests based on the multi-epoch HST ACS/WFC images reveal no significant circumstellar light echoes in between 0.3 pc and 100 pc (Yang et al. 2017) from the supernova.
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