  High statistics measurements of the photon asymmetry $\mathrm{\Sigma}$ for
the $\overrightarrow{\gamma}$p$\rightarrow\pi^{0}$p reaction have been made in
the center of mass energy range W=1214-1450 MeV. The data were measured with
the MAMI A2 real photon beam and Crystal Ball/TAPS detector systems in Mainz,
Germany. The results significantly improve the existing world data and are
shown to be in good agreement with previous measurements, and with the MAID,
SAID, and Bonn-Gatchina predictions. We have also combined the photon asymmetry
results with recent cross-section measurements from Mainz to calculate the
profile functions, $\check{\mathrm{\Sigma}}$ (= $\sigma_{0}\mathrm{\Sigma}$),
and perform a moment analysis. Comparison with calculations from the
Bonn-Gatchina model shows that the precision of the data is good enough to
further constrain the higher partial waves, and there is an indication of
interference between the very small $F$-waves and the $N(1520) 3/2^{-}$ and
$N(1535) 1/2^{-}$ resonances.
