A 9-Month $\textit{Hubble Space Telescope}$ Near-UV Survey of M87. I. Light and Color Curves of 94 Novae, and a Re-determination of the Nova Rate

M87 has been monitored with a cadence of 5 days over a 9 month-long span through the near-ultraviolet (NUV:F275W) and optical (F606W) filters of the Wide Field Camera 3 (WFC3) of the HST. This unprecedented dataset yields the NUV and optical light and color curves of 94 M87 novae, characterizing the outburst and decline properties of the largest extragalactic nova dataset in the literature (after M31). We test and confirm nova modelers' prediction that recurrent novae cannot erupt more frequently that once every 45 days; show that there are zero rapidly recurring novae in the central $\sim$ 1/3 of M87 with recurrence times $ < $ 130 days; demonstrate that novae closely follow the K-band light of M87 to within a few arcsec of the galaxy nucleus; show that nova NUV light curves are as heterogeneous as their optical counterparts, and usually peak 5 to 30 days after visible light maximum; determine our observations' detection completeness to be in the 90-96\% range; and measure the rate Rnova of nova eruptions in M87 as $325_{-38}^{+38}$/yr. The corresponding luminosity-specific classical nova rate for this galaxy is $7.06_{-.83}^{+.83}/yr/10^{10}L_\odot,_{K}$. These rates confirm that groundbased observations of extragalactic novae miss most faint, fast novae and those near the centers of galaxies.