This paper may be viewed as a sequel to [Math. Ann. 231, 97–144 (1977; Zbl 0346.10013)] where the author proved as one of his results: Let \(Q\) be an even integral quadratic form of signature \((2,q)\) and level \(n\), let \(D\) be the symmetric domain attached to \(Q\) and let \(\Gamma_ Q\) be the group of proper units for \(Q\). Then there exist elliptic cusp forms of weight \((2+q)/2\) with respect to a certain congruence subgroup of level \(n\) whose Fourier coefficients are period integrals of holomorphic \(q\)-forms on \(\Gamma_ Q\setminus D\).
In this note it is proved that there also exists an Eisenstein series of weight \((2+q)/2\) for level \(n\) whose Fourier coefficients are period integrals of certain differential forms on \(\Gamma_ Q\setminus D\) of type \((q/2,q/2)\). As the author also points out, this is in some sense a paraphrase to a result of C. L. Siegel [Indefinite quadratische Formen und Modulfunktionen, Studies Essays, pres. to R. Courant, 395–406 (1948; Zbl 0033.01304); cf. Ges. Abh., Bd. III, pp. 85–91].