# Higher congruences between newforms and Eisenstein series of squarefree level

```@article{Hsu2017HigherCB,
title={Higher congruences between newforms and Eisenstein series of squarefree level},
author={C. Hsu},
journal={arXiv: Number Theory},
year={2017}
}```
• C. Hsu
• Published 2017
• Mathematics
• arXiv: Number Theory
• Let \$p\geq 5\$ be prime. For elliptic modular forms of weight 2 and level \$\Gamma_0(N)\$ where \$N>6\$ is squarefree, we bound the depth of Eisenstein congruences modulo \$p\$ (from below) by a generalized Bernoulli number with correction factors and show how this depth detects the local non-principality of the Eisenstein ideal. We then use admissibility results of Ribet and Yoo to give an infinite class of examples where the Eisenstein ideal is not locally principal. Lastly, we illustrate these… CONTINUE READING
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