Let $D$ be a square-free positive integer which is the fundamental discriminant of a real quadratic field. Consider the following quadratic form $$Q_{D}(x,y)=x^2+Dy^2.$$ My questions are :

- What is the density of the set $\{\ell \hbox{ prime}| Q_{D}(x,y)=\ell\quad\hbox{has a solution}\}$ if it is knowen ?
- How can we use modular forms to answer such a question ? ( how to use theta series for example and distribution of eigenvlues of newforms ? )
- Thanks for any comments !