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Let K (1) be the Hilbert class field of the imaginary quadratic field K = Q(√d), d < 0. We derive the product representations of a class of Dirichlet L-series associated with the character group constructed from the Artin map between the ideal class group of K and the Galois group Gal(K (1) /K). The application of the Mellin transform to the product representations of these Dirichlet series yields a family of generating functions for representations of positive integers by the subgroups of the quadratic forms.

On separation of quadratic forms on the imaginary quadratic field in its Hilbert class field