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Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are supposedly involved in a number of glassy anomalies such as the low temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances, however direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g.~phonons). Previous studies to overcome this issue have demonstrated that the response of a glass to local force dipoles serves as a good proxy for its QLMs; we therefore study here the statistical-mechanical properties of the responses to local force dipoles in computer glasses, over a large range of glass stabilities and in various spatial dimensions, with the goal of revealing properties of the yet-inaccessible full distribution of QLMs' frequencies. We find that, as opposed to the spatial-dimension-independent universal distribution of QLMs' frequencies $ω$ (and, consequently, also of their stiffness $κ\!=\!ω^2$), the distribution of stiffnesses associated with responses to local force dipoles features a (weak) dependence on spatial dimension. We rationalize this dependence by introducing a lattice model that incorporates both the real-space profiles of QLMs --- associated with dimension-dependent long-range elastic fields --- and the universal statistical properties of their frequencies. Finally, we discuss possible connections between our findings and basic aspects of the glass transition problem, and to finite-size effects in plastic activity of ultrastable glasses.