On the computation of local components of a newform
Abstract
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 compactmodcenter 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2010
 arXiv:
 arXiv:1008.2796
 Bibcode:
 2010arXiv1008.2796L
 Keywords:

 Mathematics  Number Theory
 EPrint:
 21 pages