  We have obtained deep Hubble Space Telescope (HST) imaging of four faint and
ultra-faint dwarf galaxy candidates in the vicinity of M101 - Dw21, Dw22, Dw23
and Dw35, originally discovered by Bennet et al. (2017). Previous distance
estimates using the surface brightness fluctuation technique have suggested
that these four dwarf candidates are the only remaining viable M101 satellites
identified in ground based imaging out to the virial radius of M101 (D~250
kpc). Advanced Camera for Surveys imaging of all four dwarf candidates shows no
associated resolved stellar populations, indicating that they are thus
background galaxies. We confirm this by generating simulated HST color
magnitude diagrams of similar brightness dwarfs at the distance of M101. Our
targets would have displayed clear, resolved red giant branches with dozens of
stars if they had been associated with M101. With this information, we
construct a satellite luminosity function for M101, which is 90% complete to
M_V=-7.7 mag and 50% complete to M_V=-7.4 mag, that extends into the
ultra-faint dwarf galaxy regime. The M101 system is remarkably poor in
satellites in comparison to the Milky Way and M31, with only eight satellites
down to an absolute magnitude of M_V=-7.7 mag, compared to the 14 and 26 seen
in the Milky Way and M31, respectively. Further observations of Milky Way
analogs are needed to understand the halo-to-halo scatter in their faint
satellite systems, and connect them with expectations from cosmological
simulations.
