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Let $G$ be a finite group of Lie type. In order to determine the charactertable of $G$, Lusztig developed the theory of character sheaves. In thisframework, one has to find the transformation between two bases for the spaceof class functions on $G$, one of them being the irreducible characters of $G$,the other one consisting of characteristic functions associated to charactersheaves. In principle, this has been achieved by Lusztig and Shoji, but theunderlying process involves some scalars which are still unknown in many cases.The problem of specifying these scalars can be reduced to considering cuspidalcharacter sheaves. We will deal with the latter for the specific case where$G=E_7(q)$, and $q$ is a power of the bad prime $p=2$ for $E_7$.

On the values of unipotent characters of finite Chevalley groups of type $E_7$ in characteristic 2