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Next: Arithmetic Fields (Global)
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Features:
- This new package deals with local components of the automorphic representation
associated to a cuspidal newform. The newform is specified by giving (one component
of the NewformDecomposition of) a space of modular symbols.
Given this and a prime p, the function LocalComponent constructs the
associated admissible representation of
GL2(Qp).
- These objects have type RepLoc. The relevant verbose flag is likewise
RepLoc.
- One may compute the Conductor of an admissible representation, and
whether it IsMinimal with respect to twisting.
- One may determine whether the representation is in the principal series,
or is supercuspidal. In the first case, one may compute the
PrincipalSeriesParameters; or otherwise a CuspidalInducingDatum.
- The package also computes the local GaloisRepresentation that corresponds
to an admissible representation under the local Langlands correspondence.
(More precisely, the Galois representation is described by returning its
restriction to the inertia subgroup of a finite extension of Qp.)
Next: Arithmetic Fields (Global)
Up: Arithmetic Geometry (Modular Forms)
Previous: Modular Forms Over Imaginary
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