Exact holomorphic differentials on a quotient of the Ree curve

We produce several families of exact holomorphic differentials on a quotient X of the Ree curve in characteristic 3, defined by X:yq-y=xq0(xq-x)/Fq (where q0 = 3s, s ≥ 1 and q=3q02). We conjecture that they span the whole space of exact holomorphic differentials, and prove this in the cases s = 1 and s = 2, by calculating the kernel of the Cartier operator.