We use the large homogeneous sample of late M dwarfs, M7 to M9.5, of Ahmed &
Warren (2019) matched to $\textit{Gaia}$ DR2, to measure the relation between
absolute magnitude and spectral type, and to infer the multiplicity fraction of
the population, and the distribution of mass ratios in the binary systems.
Binaries are identified photometrically as overluminous sources. In order to
define a sample that is unbiased with respect to multiplicity we use distance
limits that are a function of $G-J$ colour to define a volume-complete sample
of 2706 systems. The $G-J$ colours are very precise, with random errors all
less than 0.02. We measure absolute magnitudes $M_J$ that are on average 0.5
mag. brighter than previous determinations. We find evidence that the
discrepancies arise from differences in spectral types in different samples.
The measured binary fraction is $16.5\pm0.8\%$, of which $98\%$ are unresolved:
both values are consistent with results of previous studies. The distribution
of excess flux in the binaries, compared to the singles, is used to infer the
mass ratio distribution $f(q)\propto q^\gamma$, where $q=M_s/M_p$. We infer a
very steep distribution over this spectral range, with $\gamma>10$ ($99\%$
probability). This says that unresolved ultracool M dwarf binaries reside
almost exclusively in equal mass systems, and implies that the spectral types
of the unresolved binaries match to with 0.5 spectral subtypes. The intrinsic
scatter in absolute magnitude $M_J$ for ultracool M dwarfs at fixed $G-J$
colour is measured to be 0.21 mag.