LMFDB - Artin representation search results

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Dimension	Conductor	Group	Root number	Parity

Smallest permutation	Ramified	Unramified primes	Ramified prime count	Frobenius-Schur

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Galois conjugate representations are grouped into single lines.

Label	Dimension	Conductor	Ramified prime count	Artin stem field	$G$	Projective image	Container	Ind	$\chi(c)$
10.695...481.30t164.b.a	$10$	$ 11^{4} \cdot 41^{6}$	$2$	6.4.2237411.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.557...000.30t164.a.a	$10$	$ 2^{8} \cdot 3^{20} \cdot 5^{4}$	$3$	6.2.4723920.2	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.722...736.30t88.a.a	$10$	$ 2^{24} \cdot 3^{16}$	$2$	6.2.1679616.2	$A_6$	$A_6$	$A_6$	$1$	$-2$
10.784...696.30t164.b.a	$10$	$ 2^{8} \cdot 3^{12} \cdot 7^{8}$	$3$	6.0.12446784.1	$S_6$	$S_6$	$S_6$	$1$	$2$
10.171...000.30t164.c.a	$10$	$ 2^{24} \cdot 3^{8} \cdot 5^{6}$	$3$	6.2.1036800.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.171...000.30t164.d.a	$10$	$ 2^{24} \cdot 3^{8} \cdot 5^{6}$	$3$	6.2.1036800.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.175...889.30t164.a.a	$10$	$ 3^{4} \cdot 167^{6}$	$2$	6.0.83667.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.251...169.30t164.a.a	$10$	$ 17^{6} \cdot 101^{4}$	$2$	6.2.29189.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.284...049.30t88.b.a	$10$	$ 3^{14} \cdot 29^{6}$	$2$	6.2.613089.1	$A_6$	$A_6$	$A_6$	$1$	$-2$
10.288...944.30t164.a.a	$10$	$ 2^{26} \cdot 3^{16}$	$2$	6.2.13436928.5	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.288...944.30t164.c.a	$10$	$ 2^{26} \cdot 3^{16}$	$2$	6.2.497664.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.365...976.30t164.a.a	$10$	$ 2^{20} \cdot 3^{20}$	$2$	6.2.7558272.2	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.424...889.30t88.a.a	$10$	$ 3^{14} \cdot 31^{6}$	$2$	6.2.700569.1	$A_6$	$A_6$	$A_6$	$1$	$-2$
10.432...144.30t164.a.a	$10$	$ 2^{6} \cdot 47^{4} \cdot 61^{4}$	$3$	6.0.45872.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.434...696.30t164.a.a	$10$	$ 2^{12} \cdot 101^{6}$	$2$	6.0.81608.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.624...625.30t164.a.a	$10$	$ 3^{14} \cdot 5^{6} \cdot 17^{4}$	$3$	6.2.309825.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.663...969.30t164.a.a	$10$	$ 3^{14} \cdot 193^{4}$	$2$	6.2.140697.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.783...296.30t164.b.a	$10$	$ 2^{24} \cdot 3^{4} \cdot 7^{8}$	$3$	6.2.3687936.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.830...000.30t164.a.a	$10$	$ 2^{6} \cdot 3^{12} \cdot 5^{12}$	$3$	6.2.9112500.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.830...000.30t164.b.a	$10$	$ 2^{6} \cdot 3^{12} \cdot 5^{12}$	$3$	6.2.9112500.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.841...201.30t164.b.a	$10$	$ 11^{6} \cdot 41^{6}$	$2$	6.4.2237411.1	$S_6$	$S_6$	$S_6$	$1$	$2$
10.879...625.30t88.a.a	$10$	$ 3^{14} \cdot 5^{6} \cdot 7^{6}$	$3$	6.2.22325625.1	$A_6$	$A_6$	$A_6$	$1$	$-2$
10.918...224.30t164.a.a	$10$	$ 2^{6} \cdot 3461^{4}$	$2$	6.2.55376.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.922...201.30t164.a.a	$10$	$ 3^{16} \cdot 11^{8}$	$2$	6.0.8732691.3	$S_6$	$S_6$	$S_6$	$1$	$2$
10.922...201.30t164.b.a	$10$	$ 3^{16} \cdot 11^{8}$	$2$	6.0.8732691.3	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.100...000.30t164.a.a	$10$	$ 2^{16} \cdot 5^{16}$	$2$	6.2.12500000.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.105...625.30t164.a.a	$10$	$ 3^{16} \cdot 5^{12}$	$2$	6.2.20503125.2	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.105...625.30t164.b.a	$10$	$ 3^{16} \cdot 5^{12}$	$2$	6.2.20503125.2	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.115...776.30t164.a.a	$10$	$ 2^{28} \cdot 3^{16}$	$2$	6.2.13436928.5	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.125...136.30t164.b.a	$10$	$ 2^{12} \cdot 3^{12} \cdot 7^{8}$	$3$	6.0.12446784.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.139...000.30t164.a.a	$10$	$ 2^{8} \cdot 3^{20} \cdot 5^{6}$	$3$	6.2.4723920.2	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.146...904.30t164.a.a	$10$	$ 2^{22} \cdot 3^{20}$	$2$	6.2.7558272.2	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.158...001.30t164.a.a	$10$	$ 3^{6} \cdot 167^{6}$	$2$	6.0.83667.1	$S_6$	$S_6$	$S_6$	$1$	$2$
10.163...000.30t164.a.a	$10$	$ 2^{26} \cdot 5^{12}$	$2$	6.2.6400000.4	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.167...824.30t164.a.a	$10$	$ 2^{6} \cdot 3^{12} \cdot 149^{4}$	$3$	6.2.193104.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.168...409.30t88.a.a	$10$	$ 3^{20} \cdot 13^{6}$	$2$	6.2.1108809.1	$A_6$	$A_6$	$A_6$	$1$	$-2$
10.201...201.30t88.b.a	$10$	$ 3^{20} \cdot 7^{8}$	$2$	6.2.15752961.1	$A_6$	$A_6$	$A_6$	$1$	$-2$
10.237...336.30t88.a.a	$10$	$ 2^{18} \cdot 67^{6}$	$2$	6.2.287296.1	$A_6$	$A_6$	$A_6$	$1$	$-2$
10.240...481.30t164.a.a	$10$	$ 3^{12} \cdot 461^{4}$	$2$	6.2.336069.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.281...329.30t164.a.a	$10$	$ 3^{14} \cdot 277^{4}$	$2$	6.2.201933.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.303...625.30t164.a.a	$10$	$ 5^{4} \cdot 191^{6}$	$2$	6.2.182405.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.311...584.30t164.a.a	$10$	$ 2^{18} \cdot 587^{4}$	$2$	6.2.37568.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.333...329.30t164.c.a	$10$	$ 3^{14} \cdot 17^{8}$	$2$	6.0.20295603.1	$S_6$	$S_6$	$S_6$	$1$	$2$
10.333...329.30t164.d.a	$10$	$ 3^{14} \cdot 17^{8}$	$2$	6.0.20295603.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.350...336.30t164.a.a	$10$	$ 2^{6} \cdot 3^{4} \cdot 17^{6} \cdot 23^{4}$	$4$	6.2.319056.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.414...256.30t164.a.a	$10$	$ 2^{24} \cdot 223^{4}$	$2$	6.2.228352.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.470...321.30t164.a.a	$10$	$ 14731^{4}$	$1$	6.0.14731.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.544...000.30t164.c.a	$10$	$ 2^{18} \cdot 3^{12} \cdot 5^{8}$	$3$	6.2.648000.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.544...000.30t164.d.a	$10$	$ 2^{18} \cdot 3^{12} \cdot 5^{8}$	$3$	6.2.648000.1	$S_6$	$S_6$	$S_6$	$1$	$-2$
10.584...616.30t164.a.a	$10$	$ 2^{24} \cdot 3^{20}$	$2$	6.4.60466176.3	$S_6$	$S_6$	$S_6$	$1$	$2$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.