Weak Weyl's law for congruence subgroups

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Let G be a connected and simply connected semisimple algebraic group over Q and let Γ⊂ G(Q) be an arithmetic subgroup. Let K∞⊂ G(R) be a maximal compact subgroup and let d be the dimension of the symmetric space G(R)/K∞. Let σ be an irreducible unitary representation of K∞. We prove that for every Γ there exists a normal subgroup Γ₁⊂ Γ of finite index such that the quotient of the counting function of the Γ₁-cuspidal spectrum of weight σ and Tᵈ/² has a positive lower bound as T→∞.