A NOTE ON EIGENVALUES OF HECKE OPERATORS ON SIEGEL MODULAR-FORMS OF DEGREE 2

Let F be a cuspidal Hecke eigenform of even weight k on Sp4(Z) with associated eigenvalues lambda-m (m is-an-element-of N). Under the assumption that its first Fourier-Jacobi coefficient does not vanish it is proved that the abscissa of convergence of the Dirichlet series SIGMA-m greater-than-or-equal-to 1 \lambda-m\m-s is less than or equal to k.