We present stellar population parameters of twelve early-type galaxies (ETGs) in the Coma Cluster based on spectra obtained using the Low Resolution Imaging Spectrograph on the Keck II Telescope. Our data allow us to examine in detail the zero-point and scatter in their stellar population properties. Our ETGs have SSP-equivalent ages of on average 5-8 Gyr with the models used here, with the oldest galaxies having ages of ~10 Gyr old. This average age is identical to the mean age of field ETGs. Our ETGs span a large range in velocity dispersion but are consistent with being drawn from a population with a single age. Specifically, ten of the twelve ETGs are consistent within their formal errors of having the same age, 5.2+/-0.2 Gyr, over a factor of more than 750 in mass. We therefore find no evidence for downsizing of the stellar populations of ETGs in the core of the Coma Cluster. We suggest that Coma Cluster ETGs may have formed the majority of their mass at high redshifts but suffered small but detectable star formation events at z~0.1-0.3. Previous detections of downsizing from stellar populations of local ETGs may not reflect the same downsizing seen in lookback studies of RSGs, as the young ages of the local ETGs represent only a small fraction of their total masses. (abridged)
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