HD106906b is an ~11$M_{mathrm{Jup}}$, ~15Myr old directly-imaged exoplanet orbiting at an extremely large distance from its host star. The wide separation (7.11 arcsec) between HD106906b and its host star greatly reduces the difficulty in direct-imaging observations, making it one of the most favorable directly-imaged exoplanets for detailed characterization. In this paper, we present HST/WFC3/IR time-resolved observations of HD106906b in the F127M, F139M, and F153M bands. We have achieved ~1% precision in the lightcurves in all three bands. The F127M lightcurve demonstrates marginally-detectable ($2.7sigma$ significance) variability with a best-fitting period of 4 hr, while the lightcurves in the other two bands are consistent with flat lines. We construct primary-subtracted deep images and use these images to exclude additional companions to HD106906 that are more massive than 4$M_{mathrm{Jup}}$ and locate at projected distances of more than ~500 au. We measure the astrometry of HD106906b in two HST/WFC3 epochs and achieve precisions better than 2.5 mas. The position angle and separation measurements do not deviate from those in the 2004 HST/ACS/HRC images for more than $1sigma$ uncertainty. We provide the HST/WFC3 astrometric results for 25 background stars that can be used as reference sources in future precision astrometry studies. Our observations also provide the first 1.4-micron water band photometric measurement for HD106906b. HD106906bs spectral energy distribution and the best-fitting BT-Settl model have an inconsistency in the 1.4-micron water absorption band, which highlights the challenges in modeling atmospheres of young planetary-mass objects.
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