  The pulsating DA white dwarfs (ZZ Ceti stars) are $g$-mode non-radial
pulsators. Asteroseismology provides strong constraints on their global
parameters and internal structure. Since all the DA white dwarfs falling in the
ZZ Ceti instability strip do pulsate, the internal structure derived from
asteroseismology brings knowledge for the DA white dwarfs as a whole group. HS
0507+0434B is one of the ZZ Ceti stars which lies approximately in the middle
of the instability strip for which we have undertaken a detailed
asteroseismological study. We carried out multisite observation campaigns in
2007 and from December 2009 to January 2010. In total, 206 hours of photometric
time-series have been collected. They have been analysed by means of Fourier
analysis and simultaneous multi-frequency sine-wave fitting. In total, 39
frequency values are resolved including 6 triplets and a number of linear
combinations. We identify the triplets as $\ell$=1 $g$-modes split by rotation.
We derived the period spacing, the rotational splitting and the rotation rate.
From the comparison of the observed periods with the theoretical periods of a
series of models we estimate the fundamental parameters of the star: its total
mass M$_{*}$/M$_{\odot}$ = 0.675, its luminosity L/L$_{\odot}$=3.5$\times
10^{-3}$, and its hydrogen mass fraction M$_{H}$/M$_{*}$= 10$^{-8.5}$.
