Nonlinear mechanics of soft materials such as polymer melts or polymer solutions are frequently investigated by Large Amplitude Oscillatory Shear (LAOS) spectroscopy tests. Less work has been reported on the characterization of the nonlinear viscoelastic properties of glassy polymers within a similar framework. In the present work, we use an extension of LAOS, i.e., mechanical spectral hole burning (MSHB), to investigate the nonlinear dynamics of an amorphous polymer in the deep glassy state. MSHB was developed as an analog to non-resonant spectral hole burning developed by Schiener et al. [Science 274(5288), 752-754 (1996)], who attributed the presence of holes to dynamic heterogeneity. On the other hand, Qin et al. [J. Polym. Sci., Part B: Polym. Phys. 47(20), 2047-2062 (2009)] in work on polymer solutions of tailored heterogeneity have attributed the presence of holes to the type of dynamics (Rouse, rubbery, etc.) rather than to a specific spatial heterogeneity. Here, we have performed MSHB experiments on poly(methyl methacrylate) in the deep glassy state (at ambient temperature, which is near to the β-relaxation) to investigate the presence and origin of holes, if any. The effects of pump frequency and pump amplitude were investigated, and we find that vertical holes could be burned successfully for frequencies from 0.0098 Hz to 0.0728 Hz and for pump amplitudes from 2% to 9% strain. On the other hand, horizontal holes were incomplete at high pump amplitude and low frequency, where higher spectral modification is observed. The results are interpreted as being related to the dynamic heterogeneity corresponding to the β-relaxation rather than to the hysteresis energy absorbed in the large deformation pump.