We present the analysis of one week of single-site high-speed CCD photometric observations of the cool ZZ Ceti star HS 0507+0434B .
Ten independent frequencies are detected in the star ’ s light variations : one singlet and three nearly-equally spaced triplets .
We argue that these triplets are due to rotationally split modes of spherical degree \ell = 1 .
This is the first detection of consistent multiplet structure in the amplitude spectrum of a cool ZZ Ceti star and it allows us to determine the star ’ s rotation period : 1.70 \pm 0.11 d .

We report exactly equal frequency , not period , spacings between the detected mode groups .
In addition , certain pairs of modes from the four principal groups have frequency ratios which are very close to 3:4 or 4:5 ; while these ratios are nearly exact ( within one part in 10 ^ { 4 } ) , they still lie outside the computed error bars .
We speculate that these relationships between different frequencies could be caused by resonances .
One of the three triplets may not be constant in amplitude and/or frequency .

We compare our frequency solution for the combination frequencies ( of which we detected 38 ) to Wu ’ s ( 1998 , 2001 ) model thereof .
We obtain consistent results when trying to infer the star ’ s convective thermal time and the inclination angle of its rotational axis .
Theoretical combination-frequency amplitude spectra also resemble those of the observations well , and direct theoretical predictions of the observed second-order light-curve distortions were also reasonably successful assuming the three triplets are due to \ell = 1 modes .
Attempts to reproduce the observed combination frequencies adopting all possible \ell = 2 identifications for the triplets did not provide similarly consistent results , supporting their identification with \ell = 1 .