Cusp forms on the exceptional group of type \(E_{7}\) (Q2797470)

Let us denote by \(G\) the exceptional Lie group of type \(E_{7,3}\) over \(\mathbb{Q}\). The purpose of the paper under the review is to construct (non-zero) holomorphic cusp forms on the corresponding bounded symmetric domain contained in \(\mathbb{C}^{27}\) for the group \(\mathrm{SL}_2\) over \(\mathbb{Q}\).NEWLINENEWLINEUsing Siegel's Eisenstein series and an idea developed by \textit{T. Ikeda} [Ann. Math. (2) 154, No. 3, 641--681 (2001; Zbl 0998.11023)], for any positive integer \(k \geq 10\), the authors construct a holomorphic cusp form of weight \(2k\) with respect to a certain arithmetic subgroup, from a Hecke cusp form in the space of elliptic cusp forms of weight \(2k-8\) with respect to \(\mathrm{SL}_2(\mathbb{Z})\).