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Direct space charge may be quantified, and hence the beam brightness observed, by measuring the quadrupolar beam modes in the CERN Proton Synchrotron (PS). The spectrum of the transverse beam size oscillations (i.e. the quadrupolar beam moment) contains valuable information: the betatron envelope modes and the coherent dispersive mode indicate optics mismatch, while their frequency shifts due to space charge allow a direct measurement thereof. To measure the quadrupolar beam moment we use thedoi:10.18429/jacow-hb2018-tha1we02 fatcat:jj6uivw6yzgvjakv2ejakznzhu