Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials

Nobuo Tsuzuki, Takuya Yamauchi

In this paper, we determine mod $2$ Galois representations ${\bar{\rho }}_{\psi ,2}:G_K:=\mathrm{Gal}(\bar{K}/K)⟶{\mathrm{GSp}}_4({\mathbb{F}}_2)$ associated to the mirror motives of rank…