  Let W be a complex reflection group. We prove that there is the maximal
finite dimensional quotient of the Hecke algebra H_q(W) of W and that the
dimension of this quotient coincides with |W|. This is a weak version of a
Brou\'e-Malle-Rouquier conjecture from 1998. The proof is based on categories O
for Rational Cherednik algebras.
