We obtained velocity dispersion and line strength index measurements for 69 faint early–type galaxies in the core of the Coma cluster. The full sample spanning $-22.0 < M_R < -17.5$ mag includes 36 dE/dS0 galaxies. We examine the $L$–$\sigma$ relation and compare it to that of bright ellipticals from the literature. The slope defined by the faint early–type galaxies including dEs/dS0s is significantly shallower, $L \propto \sigma^{2.01\pm0.36}$, than that defined by luminous elliptical galaxies, $L \propto \sigma^{4}$. Moreover, there is no evidence for a change of slope at the typical division between dwarfs and ordinary elliptical galaxies at $M_B=-18$ mag; rather, the change in slope appears at $M_B=-20.5$ mag. We show that rotation in the fainter galaxies cannot be solely responsible for the change of slope in the $L$–$\sigma$ relation. We also plot metallicity and age-dependent line strength indices in diagnostic diagrams and find that our galaxies span a wide range in both age and metallicity.