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$E_{7}$
Let 
$\mathbf{G}$ be the connected reductive group of type 
$E_{7,3}$ over 
$\mathbb{Q}$ and 
$\mathfrak{T}$ be the corresponding symmetric domain in 
$\mathbb{C}^{27}$. Let 
${\rm\Gamma}=\mathbf{G}(\mathbb{Z})$ be the arithmetic subgroup defined by Baily. In this paper, for any positive integer 
$k\geqslant 10$, we will construct a (non-zero) holomorphic cusp form on 
$\mathfrak{T}$ of weight 
$2k$ with respect to 
${\rm\Gamma}$ from a Hecke cusp form in 
$S_{2k-8}(\text{SL}_{2}(\mathbb{Z}))$. We follow Ikeda’s idea of using Siegel’s Eisenstein series, their Fourier–Jacobi expansions, and the compatible family of Eisenstein series.
