PreprintCC BY 4.0arXiv
On the evenness of coefficients of modular forms
Abstract
We study the density of primes such that ap is divisible by a prime above $2$ for modular forms f = ∑n ≥ 1 an qn of small levels. First, we reduce the problem to low weight and odd level, or a mod $2$ CM type form. Then, we provide calculations for the evenness of particular newforms. In particular, we provide a list of levels where this "evenness" can be computed exactly for all the forms with trivial nebentypus.
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BibTeX
@misc{santra2026evenness,
title = {{On the evenness of coefficients of modular forms}},
author = {Sayantan Santra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33296},
eprint = {2610.33296},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33296},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the evenness of coefficients of modular forms
AU - Sayantan Santra
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33296
UR - https://arxiv.org/abs/2610.33296
AB - We study the density of primes such that a_p is divisible by a prime above $2$ for modular forms f = ∑_n ≥ 1 a_n q^n of small levels. First, we reduce the problem to low weight and odd level, or a mod $2$ CM type form. Then, we provide calculations for the evenness of particular newforms. In particular, we provide a list of levels where this "evenness" can be computed exactly for all the forms with trivial nebentypus.
ER -