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Although links between values of finite field hypergeometric functions andeigenvalues of elliptic modular forms are well known, we establish in thispaper that there are also connections to eigenvalues of Siegel modular forms ofhigher degree. Specifically, we relate the eigenvalue of the Hecke operator ofindex $p$ of a Siegel eigenform of degree 2 and level 8 to a special value of a${}_4F_3$-hypergeometric function.

A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform