  We have carried out a study of the X-ray properties of the supernova remnant
(SNR) population in M33 with XMM-Newton, comprising deep observations of 8
fields in M33 covering all of the area within the D$_{25}$ contours, and with a
typical luminosity of 7.1$\times$10$^{34}$ erg s$^{-1}$ (0.2-2.0 keV) . Here we
report our work to characterize the X-ray properties of the previously
identified SNRs in M33, as well as our search for new X-ray detected SNRs. With
our deep observations and large field of view we have detected 105 SNRs at the
3$\sigma$ level, of which 54 SNRs are newly detected in X-rays, and three are
newly discovered SNRs. Combining XMM-Newton data with deep Chandra survey data
allows detailed spectral fitting of 15 SNRs, for which we have measured
temperatures, ionization timescales, and individual abundances. This large
sample of SNRs allows us to construct an X-ray luminosity function, and compare
its shape to luminosity functions from host galaxies of differing metallicities
and star formation rates to look for environmental effects on SNR properties.
We conclude that while metallicity may play a role in SNR population
characteristics, differing star formation histories on short timescales, and
small-scale environmental effects appear to cause more significant differences
between X-ray luminosity distributions. In addition, we analyze the X-ray
detectability of SNRs, and find that in M33 SNRs with higher [SII]/H$\alpha$
ratios, as well as those with smaller galactocentric distances, are more
detectable in X-rays.
