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The label for an Artin representation takes the form A.B.C.DcE where

  • A is the dimension of the representation;
  • B is the conductor of the representation, the format for which is explained below;
  • C is the smallest permutation representation for which this representation is a factor. If the degree is small enough, we give the degree d and t-number j in the form dtj; otherwise we use just the degree d;
  • D is an index to distinguish cases where non-Galois conjugate representations have the same dimension, conductor, and smallest permutation representation;
  • E is an index for the representation within its Galois conjugates.

The conductor is given in factored form with the following encoding. Underscores (_) are to be interpreted as multiplication signs and "e" indicates exponentiation. So, 2e3_59 converts to $2^3\cdot 59$.

Knowl status:
  • Review status: reviewed
  • Last edited by Alina Bucur on 2019-05-02 23:40:43
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