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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.02954 |
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Table of Contents:
- Let $Γ$ be a congruence subgroup of $SL_2(Z)$, and let $f$ be a normalized eigenform of weight $k$ on $Γ$. Let $K$ denote the number field generated over $Q$ by the Fourier coefficients of $f$. Let $R$ denote the the order in $K$ generated by the Fourier coefficients of $f$, which is contained in the ring of integers $O$ of $K$. We relate the primes that divide the index of $R$ in $O$ to primes $p$ such that $f$ is congruent to a conjugate of $f$ modulo a prime ideal of residue characteristic $p$. The index mentioned above is the same as the index of the quotient of the Hecke algebra by the annihilator ideal of $f$ in its normalization.