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In 2016, the first strongly lensed Type Ia supernova, iPTF16geu at redshift$z=0.409$ with four resolved images arranged symmetrically around the lensgalaxy at $z=0.2163$, was discovered. Here, refined observations of iPTF16geu,including the time delay between images, are used to decrease uncertainties inthe lens model, including the the slope of the projected surface density of thelens galaxy, $\Sigma\propto r^{1-\eta}$, and to constrain the universalexpansion rate $H_0$. Imaging with HST provides an upper limit on the slope$\eta$, in slight tension with the steeper density profiles indicated byimaging with Keck after iPTF16geu had faded, potentially due to dust extinctionnot corrected for in host galaxy imaging. Since smaller $\eta$ implies largermagnifications, we take advantage of the standard candle nature of Type Iasupernovae constraining the image magnifications, to obtain an independentconstraint of the slope. We find that a smooth lens density fails to explainthe iPTF16geu fluxes, regardless of the slope, and additional sub-structurelensing is needed. The total probability for the smooth halo model combinedwith star microlensing to explain the iPTF16geu image fluxes is maximized at$12\,\%$ for $\eta\sim 1.8$, in excellent agreement with Keck high spatialresolution data, and flatter than an isothermal halo. It also agrees perfectlywith independent constraints on the slope from lens velocity dispersionmeasurements. Combining with the observed time delays between the images, weinfer a lower bound on the Hubble constant, $H_0 \gtrsim 40\,{\rm km \ s^{-1}Mpc^{-1}}$ at $68.3\,\%$ confidence level.

Lens modelling of the strongly lensed Type Ia supernova iPTF16geu