Completeness and extent of Artin representation data (reviewed)

Data for Artin representations are complete in the following cases based on [MR:3669395, 10.1007/s40993-017-0079-5, arXiv:1610.01228]. In each case, the LMFDB contains all faithful representations for a given group and irreducible representation with conductor less than or equal to the stated bound. Representations are distinguished by their dimension, and the smallest containing permutation representation. In addition, the LMFDB contains data on Artin representations for a variety of other number fields and Galois groups.

Group Dim Container Bound $C_2$ 1 2T1 10000 $C_3$ 1 3T1 11180 $C_4$ 1 4T1 796 $C_5$ 1 5T1 752 $C_6$ 1 6T1 577 $S_3$ 2 3T2 177662241 $C_7$ 1 7T1 483 $C_8$ 1 8T1 249 $D_4$ 2 4T2 22500 $Q_8$ 2 8T5 215444 $C_9$ 1 9T1 387 $D_{5}$ 2 5T2 40000 $A_{4}$ 3 4T4 3375000 $D_{6}$ 2 6T2 22500 $D_{7}$ 2 7T2 40000 $S_{3}C_3$ 2 6T5 2828 $F_{5}$ 4 5T3 1600000000 $C_7:C_3$ 3 7T3 1000000 $S_{4}$ 3 4T5 22497 $S_{4}$ 3 6T8 635168 $A_{4}C_2$ 3 6T6 22497

Group Dim Container Bound $C_{3}^2:C_4$ 4 6T10 3374494 $S_{3}^2$ 3 6T9 7998219 $S_{4} C_2$ 3 6T11 22497 $A_{5}$ 3 12T33 66627 $A_{5}$ 4 5T4 613778 $A_{5}$ 5 6T12 52222435 $C_3^2:D_4$ 4 6T13 22500 $C_3^2:D_4$ 4 12T34 3375000 $S_{5}$ 4 5T5 7225 $S_{5}$ 4 10T12 614125 $S_{5}$ 5 6T14 52200625 $S_{5}$ 5 10T13 52200625 $S_{5}$ 6 20T30 4437053125 $A_{6}$ 5 6T15 287296 $A_{6}$ 8 36T1252 23534089616228 $A_{6}$ 9 10T26 174981250375214 $A_{6}$ 10 30T88 10077696000000000 $S_{6}$ 5 6T16 3600 $S_{6}$ 5 12T183 216000 $S_{6}$ 9 10T32 52753592444 $S_{6}$ 9 20T145 174981250375214 $S_{6}$ 10 30T176 167961600000000 $S_{6}$ 16 36T1252 553853374064674583164228907