  Using light curves and host galaxy spectra of 101 Type Ia supernovae (SNe Ia)
with redshift $z \lesssim 0.3$ from the SDSS Supernova Survey (SDSS-SN), we
derive the SN Ia rate as a function of progenitor age (the delay time
distribution, or DTD). We use the VESPA stellar population synthesis algorithm
to analyze the SDSS spectra of all galaxies in the field searched by SDSS-SN,
giving us a reference sample of 77,000 galaxies for our SN Ia hosts. Our method
does not assume any a priori shape for the DTD and therefore is minimally
parametric. We present the DTD in physical units for high stretch (luminous,
slow declining) and low stretch (subluminous, fast declining) supernovae in
three progenitor age bins. We find strong evidence of two progenitor channels:
one that produces high stretch SNe Ia $\lesssim 400$ Myr after the birth of the
progenitor system, and one that produces low stretch SNe Ia with a delay
$\gtrsim 2.4$ Gyr. We find that each channel contributes roughly half of the
Type Ia rate in our reference sample. We also construct the average spectra of
high stretch and low stretch SN Ia host galaxies, and find that the difference
of these spectra looks like a main sequence B star with nebular emission lines
indicative of star formation. This supports our finding that there are two
populations of SNe Ia, and indicates that the progenitors of high stretch SNe
are at the least associated with very recent star formation in the last few
tens of Myr. Our results provide valuable constraints for models of Type Ia
progenitors and may help improve the calibration of SNe Ia as standard candles.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics