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- W2757331841 abstract "Let $N$ and $p$ be primes such that $p$ divides the numerator of $frac{N-1}{12}$. In this paper, we study the rank $g_p$ of the completion of the Hecke algebra acting on cuspidal modular forms of weight $2$ and level $Gamma_0(N)$ at the $p$-maximal Eisenstein ideal. We give in particular an explicit criterion to know if $g_p geq 3$, thus answering partially a question of Mazur. In order to study $g_p$, we develop the theory of textit{higher Eisenstein elements}, and compute the first few such elements in four different Hecke modules. This has applications such as generalizations of the Eichler mass formula in characteristic $p$." @default.
- W2757331841 created "2017-10-06" @default.
- W2757331841 creator A5087263978 @default.
- W2757331841 date "2017-09-26" @default.
- W2757331841 modified "2023-09-27" @default.
- W2757331841 title "Higher Eisenstein elements, higher Eichler formulas and rank of Hecke algebras" @default.
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