Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are obtained. Using our theorems, some key theorems of Igusa  can be recovered.
"A character of the Siegel modular group of level 2 from theta constants." Proc. Japan Acad. Ser. A Math. Sci. 93 (8) 77 - 81, October 2017. https://doi.org/10.3792/pjaa.93.77