  We define a family of symmetric polynomials $G_{\nu,\lambda}(z_1,\cdots,
z_{n+1},q)$ indexed by a pair of dominant integral weights. The polynomial
$G_{\nu,0}(z,q)$ is the specialized Macdonald polynomial and we prove that
$G_{0,\lambda}(z,q)$ is the graded character of a level two Demazure module
associated to the affine Lie algebra $\widehat{\mathfrak{sl}}_{n+1}$. Under
suitable conditions on $(\nu,\lambda)$ (which includes the case when $\nu=0$ or
$\lambda=0$) we prove that $G_{\nu,\lambda}(z,q)$ is Schur positive and give
explicit formulae for them in terms of Macdonald polynomials.
