  Supernovae (SNe) that have been multiply-imaged by gravitational lensing are
rare and powerful probes for cosmology. Each detection is an opportunity to
develop the critical tools and methodologies needed as the sample of lensed SNe
increases by orders of magnitude with the upcoming Vera C. Rubin Observatory
and Nancy Grace Roman Space Telescope. The latest such discovery is of the
quadruply-imaged Type Ia SN 2022qmx (aka, "SN Zwicky") at $z=0.3544$. SN Zwicky
was discovered by the Zwicky Transient Facility (ZTF) in spatially unresolved
data. Here we present follow-up Hubble Space Telescope observations of SN
Zwicky, the first from the multi-cycle "LensWatch" program. We measure
photometry for each of the four images of SN Zwicky, which are resolved in
three WFC3/UVIS filters (F475W, F625W, F814W) but unresolved with
WFC3/IR~F160W, and present an analysis of the lensing system using a variety of
independent lens modeling methods. We find consistency between lens model
predicted time delays ($\lesssim1$ day), and delays estimated with the single
epoch of HST colors ($\lesssim3.5$ days), including the uncertainty from
chromatic microlensing ($\sim1$-$1.5$ days). Our lens models converge to an
Einstein radius of $\theta_E=(0.168^{+0.009}_{-0.005})\prime\prime$, the
smallest yet seen in a lensed SN system. The "standard candle" nature of SN
Zwicky provides magnification estimates independent of the lens modeling that
are brighter than predicted by $\sim1.7^{+0.8}_{-0.6}$mag and
$\sim0.9^{+0.8}_{-0.6}$mag for two of the four images, suggesting significant
microlensing and/or additional substructure beyond the flexibility of our
image-position mass models.
