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In this article, we compute the Hecke operator $\mathrm{T}_2$, associated tothe Kneser $2$-neighbours, defined on the isomorphic classes of even latticesof determinant 2, in dimension 23 and 25. In a previous article, we computedsome properties of the Satake parameters of the automorphic representations forthe linear groups discovered by Chenevier and Renard. Thanks to these results,we deduce the value of many other Hecke operators. This enables us to computefor every prime $p$ the Kneser graph associated to the $p$-neighbours oflattices in dimension 23 and 25. From our results, we improve Harder'sconjecture, and also prove many other congruences involving the Satakeparameters of the automorphic representations for the linear groups discoveredby Chenevier and Renard.

Calcul des op\'erateurs de Hecke sur les classes d'isomorphisme de r\'eseaux pairs de d\'eterminant 2 en dimension 23 et 25