Algebra restrictions modular forms Hilbert

Let be a discrete subgroup of finite covolume. We suppose that the modular curve is 'embedded' into a Hilbert modular surface, where GammaK is the Hilbert modular group associated to a real quadratic field K. We define a sequence of restrictions of Hilbert modular forms for GammaK to modular forms for Gamma. We denote by Mk1,k2(GammaK) the space of Hilbert modular forms of weight (k1,k2) for GammaK. We prove that is a subspace closed under Rankin-Cohen brackets of the space of modular forms for Gamma.