Congruence Properties of Siegel Modular Forms
نویسنده
چکیده
Let X35 be a Siegel cusp form of degree 2 and weight 35. Kikuta, Kodama and Nagaoka [4] proved that det T a(T, X35) ≡ 0 mod 23 for every half integral positive symmetric matrix T . In this paper, we give a finite number of examples of Hecke eigenforms of degree 2 and odd weights that have the same type of congruence relation above. We also introduce congruence relations for the Hecke eigenvalues of such eigenforms. We prove our main results by numerical computation. For the computation, we use Sage [5] and a Sage package for Siegel modular forms of degree two written by the author [6].
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