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Congruences modulo prime powers of Hecke eigenvalues in level $1$. (arXiv:1710.00928v3 [math.NT] UPDATED)
来源于:arXiv
We continue the study of strong, weak, and $dc$-weak eigenforms introduced by
Chen, Kiming, and Wiese. We completely determine all systems of Hecke
eigenvalues of level $1$ modulo $128$, showing there are finitely many. This
extends results of Hatada and can be considered as evidence for the more
general conjecture formulated by the author together with Kiming and Wiese on
finiteness of systems of Hecke eigenvalues modulo prime powers at any fixed
level. We also discuss the finiteness of systems of Hecke eigenvalues of level
$1$ modulo $9$, reducing the question to the finiteness of a single eigenvalue.
Furthermore, we answer the question of comparing weak and $dc$-weak eigenforms
and provide the first known examples of non-weak $dc$-weak eigenforms. 查看全文>>