The Garsia-Procesi module $R_\lambda$ has a well known basis of Artin monomials indexed by λ-subYamanouchi words, which correspond to the inv-statistic of the Haglund-Haiman-Loehr combinatorial formula for the modified Macdonald polynomials $H_\lambda(X;q,t)$ at $t=0$. We introduce a new basis for $R_\lambda$ of Garsia-Stanton descent monomials, giving a major-index type formula of the modified Hall-Littlewood polynomial $H_\lambda(x;q,t)$, and discuss the subtle connection to $H_\lambda(x;q,t)$ at $q=0$ via Robinson-Schensted-Knuth insertion. Our formula was discovered while searching for a basis of the Garsia-Haiman module by extending a similar result of Carlsson and Oblomkov for the diagonal coinvariants $DH_n$. This is joint work with E. Carlsson.