In this talk, we introduce Dirichlet series enumerating (proper) equivalence classes of full rank subforms of a given positive definite quadratic forms, focusing on the binary case. Explicit formulas linking this Dirichlet series of a quadratic form Q with Dirichlet series counting ideal classes of imaginary quadratic field associated with the quadratic form will be presented. Moreover, some analytic properties of this Dirichlet series will be introduced. This is a joint work with Seok Hyeong Lee and Seungjai Lee.