Counting newforms with prescribed ramified supercuspidal components
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911274393141248 |
|---|---|
| author | Knightly, Andrew Martin, Kimball |
| author_facet | Knightly, Andrew Martin, Kimball |
| contents | We give a formula for the number of newforms in $S_k^{\mathrm{new}}(N)$ that have prescribed ramified supercuspidal components $π_p$ at a set $T$ of primes dividing $N$. This dimension is given in terms of the trace of the Atkin--Lehner operator at $T$ on $S_k^{\mathrm{new}}(N)$. It depends only upon the weight, the level, the ramified quadratic extensions $E_p/{\mathbb Q}_p$ attached to the $π_p$, and the root number of each $π_p$. The formula is completely explicit when $T$ consists of either a single prime or all prime factors of $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting newforms with prescribed ramified supercuspidal components Knightly, Andrew Martin, Kimball Number Theory We give a formula for the number of newforms in $S_k^{\mathrm{new}}(N)$ that have prescribed ramified supercuspidal components $π_p$ at a set $T$ of primes dividing $N$. This dimension is given in terms of the trace of the Atkin--Lehner operator at $T$ on $S_k^{\mathrm{new}}(N)$. It depends only upon the weight, the level, the ramified quadratic extensions $E_p/{\mathbb Q}_p$ attached to the $π_p$, and the root number of each $π_p$. The formula is completely explicit when $T$ consists of either a single prime or all prime factors of $N$. |
| title | Counting newforms with prescribed ramified supercuspidal components |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.14587 |