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We present the complete set of {\it Hubble Space Telescope} imaging of thebinary neutron star merger GW170817 and its optical counterpart AT 2017gfo.Including deep template imaging in F814W, F110W, F140W, and F160W at 3.4 yearspost-merger, we re-analyze the full light curve of AT 2017gfo across 12 bandsfrom 5--1273 rest-frame days after merger. We obtain four new detections of theshort $\gamma$-ray burst (GRB) 170817A afterglow from 109--170 rest-frame dayspost-merger. These detections are consistent with the previously observed$\beta=-0.6$ spectral index in the afterglow light curve with no evidence forspectral evolution. We also analyze our limits in the case of novel late-timeoptical and IR emission signatures, such as a kilonova afterglow or infrareddust echo, but find our limits are not constraining in these contexts. We usethe new data to construct deep optical and infrared stacks, reaching limits of$M=-6.3$ to $-4.6$ mag, to analyze the local environment around AT 2017gfo andlow surface brightness features in its host galaxy NGC 4993. We rule out thepresence of any globular cluster at the position of AT 2017gfo to $2.3 \times10^{4} L_{\odot}$, including those with the reddest $V-H$ colors. Finally, weanalyze the substructure of NGC 4993 in deep residual imaging, and find shellfeatures which extend up to 71.8\arcsec\ (14.2 kpc) from the center of thegalaxy. We find that the shells have a cumulative stellar mass of$6.3\times10^{8} M_{\odot}$, roughly 2% the total stellar mass of NGC 4993, andmass-weighted ages of $>$3 Gyr. We conclude that it was unlikely the GW170817progenitor system formed in the galaxy merger, which based on dynamicalsignatures and the stellar population in the shells mostly likely occurred220--685 Myr ago.

Deep Hubble Space Telescope Observations of GW170817: Complete Light Curves and the Properties of the Galaxy Merger of NGC 4993