  We report on the analysis of 34 years of photometric observations of the
pulsating helium atmosphere white dwarf GD358. The complete data set includes
archival data from 1982-2006, and 1195.2 hours of new observations from 2007-
2016. From this data set, we extract 15 frequencies representing g-mode
pulsation modes, adding 4 modes to the 11 modes known previously. We present
evidence that these 15 modes are ell = 1 modes, 13 of which belong to a
consecutive sequence in radial overtone k. We perform a detailed asteroseismic
analysis using models that include parameterized, complex carbon and oxygen
core composition profiles to fit the periods. Recent spectroscopic analyses
place GD358 near the red edge of the DBV instability strip, at 24,000 plus or
minus 500 K and a log g of 7.8 plus or minus 0.08 dex. The surface gravity
translates to a mass range of 0.455 to 0.540 solar masses. Our best fit model
has a temperature of 23,650 K and a mass of 0.5706 solar masses. That is
slightly more massive than suggested by most the recent spectroscopy. We find a
pure helium layer mass of 10^-5.50, consistent with the result of previous
studies and the outward diffusion of helium over time.
