Quasiinvariants of $S_3$

Let $s_{ij}$ represent a tranposition in $S_n$. A polynomial $P$ in $\mathbb{Q}[X_n]$ is said to be $m$-quasiinvariant with respect to $S_n$ if $(x_i-x_j{)}^{2m+1}$ divides $(1-s_{ij})P$ for all $1\le i,j\le n$. We call the ring $m$-quasiinvariants $Q{I}_m[X_n]$. We describe a method for constructing a basis for the quotient $Q{I}_m[X_3]\mathrm{/}<e_1,e_2,e_3>$. This leads to the evaluation of certain binomial determinants that are interesting in their own right.