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In [1] a conjecture for the modular transformation of the free fermiongeneralised Gibbs ensemble (GGE) was given where only the KdV charge associatedto the weight four quasi primary field was inserted. In this paper we firstgeneralise this conjecture to the case with an arbitrary, finite collection ofKdV charges in the GGE. These GGEs are generalisations of the generatingfunction of power partitions. We prove the conjectured transformation for thecase with a finite number of charges inserted and discuss the case with aninfinite number of charges.

Modular transform of free fermion generalised Gibbs ensembles and generalised power partitions