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 } .