We have obtained FUSE and HST STIS time-resolved spectroscopy of the Polar AM Herculis during a deep low state. The spectra are entirely dominated by the emission of the white dwarf. Both the far-ultraviolet ( FUV ) flux and the spectral shape vary substantially over the orbital period, with maximum flux occurring at the same phase as during the high state. The variations are due to the presence of a hot spot on the white dwarf, which we model quantitatively. The white dwarf parameters can be determined from a spectral fit to the faint-phase data, when the hot spot is self-eclipsed. Adopting the distance of 79 þ8 À6 pc determined by Thorstensen, we find an effective temperature of 19;800 AE 700 K and a mass of M WD ¼ 0:78 þ 0:12 À 0:17 M . The hot spot has a lower temperature than during the high state, $34,000-40,000 K, but covers a similar area, $10% of the white dwarf surface. Low-state FUSE and STIS spectra taken during four different epochs in [2002][2003] show no variation of the FUV flux level or spectral shape, implying that the white dwarf temperature and the hot spot temperature, size, and location do not depend on the amount of time the system has spent in the low state. Possible explanations are ongoing accretion at a low level or deep heating; both alternatives have some weaknesses, which we discuss. No photospheric metal absorption lines are detected in the FUSE and STIS spectra, suggesting that the average metal abundances in the white dwarf atmosphere are lower than $10 À3 times their solar values.