On the computation of local components of a newform

Details On the computation of local components of a newform On the computation of local components of a newform

2010-08-17

arxiv.org/abs/1008.2796v1

Mathematics

Number Theory

21 pages

Scientific paper

We present an algorithm for computing the $p$-component of the automorphic representation arising from a cuspidal newform $f$ for a prime $p$. This is equivalent to computing the restriction to the decomposition group at $p$ of the $\ell$-adic Galois representations attached to $f$ for any $\ell\neq p$. The situation is most interesting when $p^2$ divides the level of $f$, in which case the $p$-component could be supercuspidal. In the supercuspidal case, the local component is induced from an irreducible character of a compact-mod-center subgroup of $\text{GL}_2(\mathbf{Q}_p)$; our algorithm outputs both the group and the irreducible character. We provide examples which illustrate how the local Galois representation can be completely read off from the local component.

Affiliated with

Also associated with

No associations

Rating

On the computation of local components of a newform does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the computation of local components of a newform, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the computation of local components of a newform will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-397172