Given a partition \(\lambda \vdash n\), the modified Macdonald polynomials \(\widetilde{H}_\lambda(X;q,t)\) are a family of symmetric functions over \(\mathbb{C}(q,t)\) that are ubiquitous in representation theory, with many interesting specializations. In 1992, Garsia and Haiman constructed a family of modules \(V_\lambda\) that was conjectured to carry the representation of \(\widetilde{H}_\lambda(X;q,t)\), and in 2001 Haiman completed the proof by showing the vector space dimension of \(V_\lambda\) is \(n!\), a fact that was ultimately proved geometrically. It is an open problem to construct an explicit vector space basis of \(\widetilde{H}_\lambda(X;q,t)\). We discuss partial vector space bases for \(V_\lambda\) based on the combinatorial formula for \(\widetilde{H}_\lambda(X;q,t)\) due to Haglund-Haiman-Loehr, in particular the \(q = 0\) component (known as the Garsia-Procesi module, joint work with E. Carlsson) and maximal \(t\)-degree.