  Using the improved lower bound on the sum of the eigenvalues of the Dirichlet
Laplacian proved by A. D. Melas (Proc. Amer. Math. Soc. \textbf{131} (2003)
631-636), we report a new and sharp estimate for the dimension of the global
attractor associated to the complex Ginzburg-Landau equation supplemented with
Dirichlet boundary conditions.
