  We have obtained optical spectra of 29 early-type (E/S0) galaxies that hosted
type Ia supernovae (SNe Ia). We have measured absorption-line strengths and
compared them to a grid of models to extract the relations between the
supernova properties and the luminosity-weighted age/composition of the host
galaxies. The same analysis was applied to a large number of early-type field
galaxies selected from the SDSS spectroscopic survey. We find no difference in
the age and abundance distributions between the field galaxies and the SN Ia
host galaxies. We do find a strong correlation suggesting that SNe Ia in
galaxies whose populations have a characteristic age greater than 5 Gyr are ~ 1
mag fainter at V(max) than those found in galaxies with younger populations.
However, the data cannot discriminate between a smooth relation connecting age
and supernova luminosity or two populations of SN Ia progenitors. We find that
SN Ia distance residuals in the Hubble diagram are correlated with host-galaxy
metal abundance, consistent with the predictions of Timmes, Brown & Truran
(2003). The data show that high iron abundance galaxies host less-luminous
supernovae. We thus conclude that the time since progenitor formation primarily
determines the radioactive Ni production while progenitor metal abundance has a
weaker influence on peak luminosity, but one not fully corrected by light-curve
shape and color fitters. Assuming no selection effects in discovering SNe Ia in
local early-type galaxies, we find a higher specific SN Ia rate in E/S0
galaxies with ages below 3 Gyr than in older hosts. The higher rate and
brighter luminosities seen in the youngest E/S0 hosts may be a result of recent
star formation and represents a tail of the "prompt" SN Ia progenitors.
