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 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 $2^3\cdot 59$.