  We present a detailed strong lensing analysis of an HST/ACS legacy dataset
for the first gravitational lens, Q0957+561. With deep imaging we identify 24
new strongly lensed features, which we use to constrain mass models. We model
the stellar component of the lens galaxy using the observed luminosity
distribution, and the dark matter halo using several different density
profiles. We draw on the weak lensing analysis by Nakajima et al. (2009) to
constrain the mass sheet and environmental terms in the lens potential.
Adopting the well-measured time delay, we find H_0 = 85 (+14/-13) km/s/Mpc (68%
CL) using lensing constraints alone. The principal uncertainties in H_0 are
tied to the stellar mass-to-light ratio (a variant of the radial profile
degeneracy in lens models). Adding constraints from stellar population
synthesis models, we obtain H_0 = 79.3 (+6.7/-8.5) km/s/Mpc (68% CL). We infer
that the lens galaxy has a rising rotation curve and a dark matter distribution
with an inner core. Intriguingly, we find the quasar flux ratios predicted by
our models to be inconsistent with existing radio measurements, suggesting the
presence of substructure in the lens.
