UPPER BOUND ON THE NUMBER OF SYSTEMS OF HECKE EIGENVALUES FOR SIEGEL MODULAR FORMS (MOD p)
نویسنده
چکیده
. The constants are effectively computable. Proof. Part (a) follows from the fact that the algebraic group GSp2g has dimension 2g +g+1. Part (b) is obvious. Combined with Theorem 1.1 of [Ghi04], Theorem 1 gives Corollary 3 (Algebraic modular forms). Let B/Q be the quaternion algebra ramified at p and ∞. The number of systems of Hecke eigenvalues coming from algebraic modular forms (mod p) of level N on GUg(B) satisfies the inequality of Theorem 1.
منابع مشابه
Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms
In his letter (Serre, 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → Fp, where B is the endomorphism algebra of a supersingular elliptic curve. We generalize this result to Siegel modular forms, proving that the systems of Hecke eigenvalues given by Siegel modular forms (mod p)...
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