  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 $\omega$ (and, consequently, also of their
stiffness $\kappa\!=\!\omega^2$), 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.
