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We prove general type results for orthogonal modular varieties associatedwith the moduli of compact hyperk\"ahler manifolds of deformation generalisedKummer type ('deformation generalised Kummer varieties'). In particular, weconsider moduli spaces of deformation generalised Kummer fourfolds withsplit-polarisation of degree $2d$. Our main result is that when $d$ is prime or$2d$ is square-free then the associated modular varieties are of general typewhen $d$ exceeds bounds we determine, subject to the existence of certainlow-weight cusp forms for $\operatorname{O}(2,n)$. As a corollary, we concludethat the corresponding moduli spaces are also of general type.

On the Kodaira Dimension of the Moduli of Deformation Generalised Kummer Varieties