  Using a penalised maximum likelihood we estimate, for the first time, the
velocity distribution of white dwarfs in the Solar neighbourhood. Our sample
consists of 129 675 white dwarfs within 500 pc in Gaia Early Data Release 3 The
white dwarf velocity distributions reveal a similar structure to the rest of
the Solar neighbourhood stars, reflecting that white dwarfs are subjected to
the same dynamical processes. In the velocity distribution for three
magnitude-binned subsamples we however find a novel structure at $(U, V) = (7,
-19)$ km s$^{-1}$ in fainter samples, potentially related to the Coma Berenices
stream. We also see a double-peaked feature in $U$-$W$ at $U \approx -30$ km
s$^{-1}$ and in $V$-$W$ at $V \approx -20$ km s$^{-1}$ for fainter samples. We
determine the velocity distribution and velocity moments as a function of
absolute magnitude for two samples based on the bifurcation identified in Gaia
Data Release 2 in the colour-magnitude diagram. The brighter, redder sequence
has a larger velocity dispersion than the fainter, bluer sequence across all
magnitudes. It is hard to reconcile this kinematic difference with a
bifurcation caused purely by atmospheric composition, while it fits neatly with
a significant age difference between the two sequences. Our results provide
novel insights into the kinematic properties of white dwarfs and demonstrate
the power of analytical techniques that work for the large fraction of stars
that do not have measured radial velocities in the current era of large-scale
astrometric surveys.
