  We present Hubble Space Telescope observations and photometric measurements
of the Type Ia supernova (SN Ia) SN 2013aa 1500 days after explosion. At this
epoch, the luminosity is primarily dictated by the amounts of radioactive
${}^{57}\textrm{Co}$ and ${}^{55}\textrm{Fe}$, while at earlier epochs, the
luminosity depends on the amount of radioactive ${}^{56}\textrm{Co}$. The ratio
of odd-numbered to even-numbered isotopes depends significantly on the density
of the progenitor white dwarf during the SN explosion, which, in turn, depends
on the details of the progenitor system at the time of ignition. From a
comprehensive analysis of the entire light curve of SN 2013aa, we measure a
$M({}^{57}\textrm{Co})/M({}^{56}\textrm{Co})$ ratio of $0.02^{+0.01}_{-0.02}$,
which indicates a relatively low central density for the progenitor white dwarf
at the time of explosion, consistent with double-degenerate progenitor
channels. We estimate $M({}^{56}\textrm{Ni}) = 0.732 \pm
0.151\:\mathrm{M_{\odot}}$, and place an upper limit on the abundance of
${}^{55}\textrm{Fe}$. A recent study reported a possible correlation between
$M({}^{57}\textrm{Co})/M({}^{56}\textrm{Co})$ and stretch for four SNe Ia. SN
2013aa, however, does not fit this trend, indicating either SN 2013aa is an
extreme outlier or the correlation does not hold up with a larger sample. The
$M({}^{57}\textrm{Co})/M({}^{56}\textrm{Co})$ measured for the expanded sample
of SNe Ia with photometry at extremely late times has a much larger range than
that of explosion models, perhaps limiting conclusions about SN Ia progenitors
drawn from extremely late-time photometry.
