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We investigate the mass structure of a strong gravitational lens galaxy at$z=0.350$, taking advantage of the milli-arcsecond (mas) angular resolution ofvery long baseline interferometric (VLBI) observations. In the first analysisof its kind at this resolution, we jointly infer the lens model parameters andpixellated radio source surface brightness. We consider several lens models ofincreasing complexity, starting from an elliptical power-law density profile.We extend this model to include angular multipole structures, a separatestellar mass component, additional nearby field galaxies, and/or a genericexternal potential. We compare these models using their relative Bayesianlog-evidence (Bayes factor). We find strong evidence for angular structure inthe lens; our best model is comprised of a power-law profile plus multipoleperturbations and external potential, with a Bayes factor of $+14984$ relativeto the elliptical power-law model. It is noteworthy that the ellipticalpower-law mass distribution is a remarkably good fit on its own, withadditional model complexity correcting the deflection angles only at the$\sim5$ mas level. We also consider the effects of added complexity in the lensmodel on time-delay cosmography and flux-ratio analyses. We find that an overlysimplistic power-law ellipsoid lens model can bias the measurement of $H_0$ by$\sim3$ per cent and mimic flux ratio anomalies of $\sim8$ per cent. Ourresults demonstrate the power of high-resolution VLBI observations to providestrong constraints on the inner density profiles of lens galaxies.

A lensed radio jet at milli-arcsecond resolution I: Bayesian comparison of parametric lens models