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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 betweenabsolute magnitude and spectral type, and to infer the multiplicity fraction ofthe population, and the distribution of mass ratios in the binary systems.Binaries are identified photometrically as overluminous sources. In order todefine a sample that is unbiased with respect to multiplicity we use distancelimits that are a function of $G-J$ colour to define a volume-complete sampleof 2706 systems. The $G-J$ colours are very precise, with random errors allless than 0.02. We measure absolute magnitudes $M_J$ that are on average 0.5mag. brighter than previous determinations. We find evidence that thediscrepancies 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 distributionof excess flux in the binaries, compared to the singles, is used to infer themass ratio distribution $f(q)\propto q^\gamma$, where $q=M_s/M_p$. We infer avery steep distribution over this spectral range, with $\gamma>10$ ($99\%$probability). This says that unresolved ultracool M dwarf binaries residealmost exclusively in equal mass systems, and implies that the spectral typesof the unresolved binaries match to with 0.5 spectral subtypes. The intrinsicscatter in absolute magnitude $M_J$ for ultracool M dwarfs at fixed $G-J$colour is measured to be 0.21 mag.

The absolute magnitudes $M_J$, the binary fraction, and the binary mass ratios of M7 to M9.5 dwarfs