PreprintCC BY-NC-SA 4.0arXiv
Prime-power congruences for level-one eigenforms
Abstract
We study prime-power congruences for the prime-to-p Hecke eigensystems of normalized cuspidal level-one eigenforms as the weight varies, and we address the problem of classifying such systems for small prime powers. We construct Hecke-equivariant transfer maps between level-one modular-symbol modules via multiplication by suitable lifts of Dickson invariants; these maps reduce the problem to finite computation and propagate Hecke operator relations through all weights. For p=2,3,5,7, we obtain all-weight classifications modulo 28, 34, 53, and 72, respectively.
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BibTeX
@misc{rustom2026primepower,
title = {{Prime-power congruences for level-one eigenforms}},
author = {Nadim Rustom},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16750},
eprint = {2609.16750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16750},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Prime-power congruences for level-one eigenforms
AU - Nadim Rustom
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16750
UR - https://arxiv.org/abs/2609.16750
AB - We study prime-power congruences for the prime-to-p Hecke eigensystems of normalized cuspidal level-one eigenforms as the weight varies, and we address the problem of classifying such systems for small prime powers. We construct Hecke-equivariant transfer maps between level-one modular-symbol modules via multiplication by suitable lifts of Dickson invariants; these maps reduce the problem to finite computation and propagate Hecke operator relations through all weights. For p=2,3,5,7, we obtain all-weight classifications modulo 2^8, 3^4, 5^3, and 7^2, respectively.
ER -