Let $\mathcal{S}$ be the set of all positive definite binary quadratic forms with integer coefficients. Define the action of the group $S L_{2}(\mathbb{Z})$ on $\mathcal{S}$, and prove that equivalent forms under this action have the same discriminant.

Find necessary and sufficient conditions for an odd positive integer $n$, prime to 35 , to be properly represented by at least one of the two forms

$$x^{2}+x y+9 y^{2}, \quad 3 x^{2}+x y+3 y^{2}$$