The dwarf nova GW Librae (GW Lib) is the first cataclysmic variable (CV) discovered to have a primary in a white dwarf instability strip, making it the first multimode, non-radially pulsating star known to be accreting. The primaries of CVs, embedded in hot, bright accretion discs, are difficult to study directly. Applying the techniques of asteroseismology to GW Lib could therefore give us an unprecedented look at a white dwarf that has undergone ~109 yr of accretion. However, an accreting white dwarf may have characteristics sufficiently different from those of single pulsating white dwarfs to render the standard models of white dwarf pulsations invalid for its study. This paper presents amplitude spectra of GW Lib from a series of observing campaigns conducted during 1997, 1998 and 2001. We find that the dominant pulsation modes cluster at periods near 650, 370 and 230 s, which also appear in linear combinations with each other. The pulsation spectrum of GW Lib is highly unstable on time-scales of months, and exhibits clusters of signals very closely spaced in frequency, with separations on the order of 1 μHz.