A well-known formula of Whipple relates certain hypergeometric values $$_7F_6(1)$$ and $$_4F_3(1)$$ . In this paper, we revisit relation from the viewpoint underlying data HD, to which there are also associated character sums Galois representations. We explain a special structure behind Whipple’s when HD primitive self-dual. If defined over $$\mathbb Q$$ , by work Katz, Beukers, Cohen, Mellit, ...