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In this article, we determine the trace of some Hecke operators on the spacesof level one automorphic forms on the special orthogonal groups of theeuclidean lattices $\mathrm{E}_7$, $\mathrm{E}_8$ and $\mathrm{E}_8\oplus\mathrm{A}_1$, with arbitrary weight. Using Arthur's theory, we deduceproperties of the Satake parameters of the automorphic representations for thelinear groups discovered by Chenevier and Renard. Our results corroborate aconjecture by Bergstr\"om, Faber and van der Geer about the Hasse-Weil zetafunction on the moduli spaces of $17$-pointed curves of genus $3$.

Traces des op\'erateurs de Hecke sur les espaces de formes automorphes  de $\mathrm{SO}_7$, $\mathrm{SO}_8$ ou $\mathrm{SO}_9$ en niveau $1$ et poids  arbitraire