  We present the luminosity function (LF) and measurements of the scalelengths,
colours, and radial distribution of dwarf galaxies in the Coma cluster down to
R=24. Our survey area is 674 arcmin^2; this is the deepest and most detailed
survey covering such a large area. Our measurements agree with those of most
previous authors at bright and intermediate magnitudes. The new results are: 1)
Galaxies in the Coma cluster have a luminosity function that is steep (\alpha
\sim -1.7) for -15 < M_R < -11, and is shallower brighter than this. The
curvature in the LF at M_R \sim -15 is statistically significant. 2) The
galaxies that contribute most strongly to the luminosity function at -14 < M_R
< -12 have colours and scalelengths that are consistent with those of local
dwarf spheroidal galaxies placed at the distance of Coma. 3) These galaxies
with -14 < M_R < -12 have a colour distribution that is very strongly peaked at
B-R = 1.3. This is suggestive of a substantial degree of homogeneity in their
star formation histories and metallicities. 4) These galaxies with -14 < M_R <
-12 also appear to be more confined to the cluster core (r \sim 200 kpc) than
the brighter galaxies.
