A new model for the description of beam instabilities in synchrotrons featuring wakefields and space charge forces is proposed, using the circulant matrix approach. The predictions of this model are discussed in light of past ones, with a particular emphasis on the possible mitigation of the transverse mode coupling instability by space charge forces. The existence of transient amplification in spite of the absence of unstable eigenvalues in configuration featuring strong space charge forces is also addressed. It is shown that this behavior can be recovered when considering an airbag distribution. Yet when considering a more realistic Gaussian distribution, the radial modes lead to other types of mode coupling instabilities. The predictions of the new model are then compared to results of an experiment conducted at the CERN Super Proton Synchrotron, showing a reasonable agreement.