Let \(\Gamma_n(K)\) stand for the Siegel modular group if \(K=\mathbb{Q}\) resp. for the Hermitian modular group of degree \(n\) over \(K\) if \(K\) is an imaginary quadratic number field of class number 1. Denote by \(E^{(n)}_{k,K} (Z,s)\) the attached Siegel-Eisenstein series of weight \(k\) with factor of convergence \((\text{det Im} M \langle Z \rangle)^s\). Using \textit{G. Shimura}'s result [Duke Math. J. 50, 417-476 (1983; Zbl 0519.10019)] the author obtains a modular form of weight \(k\) with rational Fourier coefficients, whenever \(k\) is even, \(k<{n+1 \over 2}\) resp. \(k