We present near-infrared emission line counts and luminosity functions from the HST WFC3 Infrared Spectroscopic Parallels (WISP) program for 29 fields (0.037 deg^2) observed using both the G102 and G141 grisms. Altogether we identify 1048 emission line galaxies with observed equivalent widths greater than 40 Angstroms, 467 of which have multiple detected emission lines. The WISP survey is sensitive to fainter flux levels (3-5x10^-17 ergs/s/cm^2) than the future space near-infrared grism missions aimed at baryonic acoustic oscillation cosmology (1-4x10^-16 ergs/s/cm^2), allowing us to probe the fainter emission line galaxies that the shallower future surveys may miss. Cumulative number counts of 0.7<z<1.5 galaxies reach 10,000 deg^-2 above an H-alpha flux of 2x10^-16 ergs/s/cm^2. H-alpha-emitting galaxies with comparable [OIII] flux are roughly 5 times less common than galaxies with just H-alpha emission at those flux levels. Galaxies with low H-alpha/[OIII] ratios are very rare at the brighter fluxes that future near-infrared grism surveys will probe; our survey finds no galaxies with H-alpha/[OIII] < 0.95 that have H-alpha flux greater than 3x10^-16 ergs/s/cm^2. Our H-alpha luminosity function contains a comparable number density of faint line emitters to that found by the NICMOS near-infrared grism surveys, but significantly fewer (factors of 3-4 less) high luminosity emitters. We also find that our high redshift (z=0.9-1.5) counts are in agreement with the high redshift (z=1.47) narrow band H-alpha survey of HiZELS (Sobral et al. 2013), while our lower redshift luminosity function (z=0.3-0.9) falls slightly below their z=0.84 result. The evolution in both the H-alpha luminosity function from z=0.3--1.5 and the [OIII] luminosity function from z=0.7-2.3 is almost entirely in the L* parameter, which steadily increases with redshift over those ranges.
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