  (abr.) We present the analysis of the spectroscopic catalog of galaxies in
the Coma cluster from Mobasher et al. This catalog comprises ~300 spectra of
cluster members with magnitudes M_B=-20.5 to -14 in two areas of ~1 X 1.5 Mpc
towards the center and the SW region of the cluster. In this paper the analysis
is restricted to the 257 galaxies with no emission lines in their spectra. The
strength of the age-sensitive indices is found to correlate with galaxy
magnitude over the whole magnitude range. Similarly, the metallicity-sensitive
indices anticorrelate with magnitude. By comparing the observed indices with
model grids based on the Padova isochrones, we derive luminosity-weighted ages
and metallicities. We present the distributions of ages and metallicities for
galaxies in various magnitude bins. The mean metallicity decreases with galaxy
magnitude and, at a given luminosity, appears to be generally lower for
galaxies in the SW region of Coma as compared to the center of the cluster. A
broad range of ages, from younger than 3 Gyr to older than 9 Gyr, is found in
galaxies of any magnitude. However, systematic trends of age with luminosity
are present among galaxies in the central field. In the central Mpc of Coma, a
large fraction of galaxies at any luminosity (50-60% of the giants, >30 % of
the dwarfs) show no evidence in their central regions of star formation
occurred at redshift z<2, while the proportion of galaxies with significant
star formation occurring at intermediate (0.35<z<2) and low (z<0.35) redshifts
is found to depend on galaxy luminosity. Faint galaxies with young
luminosity-weighted ages appear to have a bimodal metallicity distribution
that, if confirmed, would point to a composite formation scenario. Finally, we
present an interpretation of the index-magnitude relations observed.
