This talk is based on a recent joint work with Wen-Ching Winnie Li and Ling Long. We consider the hypergeometric data corresponding to a formula due to Whipple which relates certain hypergeometric values \(_7F_6(1)\) and \(_4F_3(1)\). When the hypergeometric data are primitive and defined over \(\mathbb Q\), from identities of hypergeometric character sums, we explain a special structure of the corresponding Galois representations behind Whipple’s formula leading to a decomposition that can be described by the Fourier coefficients of Hecke eigenforms. In this talk, I will use an example to demonstrate our approach and relate the hypergeometric values to certain periods of modular forms.