  We report the discovery of 40 new satellite dwarf galaxy candidates in the
sphere of influence of the Sombrero galaxy (M104) the most luminous galaxy in
the Local Volume. Using the Subaru Hyper Suprime-Cam, we surveyed 14.4 square
degrees of its surroundings, extending to the virial radius. Visual inspection
of the deep images and GALFIT modelling yielded a galaxy sample highly complete
down to $M_{g}\sim-9$ ($L_{g}\sim3\times 10^{5}\,L_\odot$) and spanning
magnitudes $-16.4 < M_g < -8$ and half-light radii $50\,pc\ <\ r_e\ <\
1600\,pc$ assuming the distance of M104. These 40 new, out of which 27 are
group members with high confidence, double the number of potential satellites
of M104 within the virial radius, placing it among the richest hosts in the
Local Volume. Using a Principle Component Analysis (PCA), we find that the
entire sample of candidates consistent with an almost circular on-sky
distribution, more circular than any comparable environment found in the
Illustris TNG100-1 simulation. However the distribution of the high probability
sample is more oblate and consistent with the simulation. The cumulative
satellite luminosity function is broadly consistent with analogues from the
simulation, albeit it contains no bright satellite with $M_{g}<-16.4$
($L_{g}\sim3 \times 10^{8}\,L_\odot$), a $2.3\,\sigma$ occurrence. Follow-up
spectroscopy to confirm group membership will begin to demonstrate how these
systems can act as probes of the structure and formation history of the halo of
M104.
