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

Projective image	Projective image type

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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	$\chi(c)$
2.39.4t3.a.a	$2$	$3 \cdot 13$	$2$	4.0.117.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.55.4t3.c.a	$2$	$5 \cdot 11$	$2$	4.2.275.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.56.4t3.b.a	$2$	$2^{3} \cdot 7$	$2$	4.0.392.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.63.4t3.a.a	$2$	$3^{2} \cdot 7$	$2$	4.0.189.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.68.4t3.a.a	$2$	$2^{2} \cdot 17$	$2$	4.0.272.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.80.4t3.a.a	$2$	$2^{4} \cdot 5$	$2$	4.0.320.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.95.4t3.c.a	$2$	$5 \cdot 19$	$2$	4.2.475.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.111.4t3.a.a	$2$	$3 \cdot 37$	$2$	4.0.333.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.128.4t3.a.a	$2$	$2^{7}$	$1$	4.0.512.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.136.4t3.a.a	$2$	$2^{3} \cdot 17$	$2$	4.0.1088.2	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$-2$
2.136.4t3.b.a	$2$	$2^{3} \cdot 17$	$2$	4.0.1088.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.144.4t3.b.a	$2$	$2^{4} \cdot 3^{2}$	$2$	4.0.432.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.145.4t3.b.a	$2$	$5 \cdot 29$	$2$	4.4.725.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$2$
2.155.4t3.c.a	$2$	$5 \cdot 31$	$2$	4.2.775.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.164.4t3.c.a	$2$	$2^{2} \cdot 41$	$2$	4.0.656.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.171.4t3.c.a	$2$	$3^{2} \cdot 19$	$2$	4.0.513.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.183.4t3.a.a	$2$	$3 \cdot 61$	$2$	4.0.549.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.184.4t3.c.a	$2$	$2^{3} \cdot 23$	$2$	4.2.1472.2	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.196.4t3.a.a	$2$	$2^{2} \cdot 7^{2}$	$2$	4.0.1372.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.203.4t3.a.a	$2$	$7 \cdot 29$	$2$	4.0.1421.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.205.4t3.a.a	$2$	$5 \cdot 41$	$2$	4.0.1025.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$-2$
2.208.4t3.c.a	$2$	$2^{4} \cdot 13$	$2$	4.0.832.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.219.4t3.c.a	$2$	$3 \cdot 73$	$2$	4.0.657.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.221.4t3.b.a	$2$	$13 \cdot 17$	$2$	4.0.2873.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$-2$
2.224.4t3.a.a	$2$	$2^{5} \cdot 7$	$2$	4.0.1568.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.248.4t3.c.a	$2$	$2^{3} \cdot 31$	$2$	4.2.1984.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.256.4t3.c.a	$2$	$2^{8}$	$1$	4.2.2048.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.259.4t3.a.a	$2$	$7 \cdot 37$	$2$	4.0.1813.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.260.4t3.a.a	$2$	$2^{2} \cdot 5 \cdot 13$	$3$	4.0.1040.2	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.260.4t3.b.a	$2$	$2^{2} \cdot 5 \cdot 13$	$3$	4.0.1040.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.264.4t3.c.a	$2$	$2^{3} \cdot 3 \cdot 11$	$3$	4.0.2112.2	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.264.4t3.d.a	$2$	$2^{3} \cdot 3 \cdot 11$	$3$	4.0.2112.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.275.4t3.c.a	$2$	$5^{2} \cdot 11$	$2$	4.2.1375.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.276.4t3.e.a	$2$	$2^{2} \cdot 3 \cdot 23$	$3$	4.2.3312.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.276.4t3.f.a	$2$	$2^{2} \cdot 3 \cdot 23$	$3$	4.2.3312.2	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.279.4t3.b.a	$2$	$3^{2} \cdot 31$	$2$	4.0.837.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.291.4t3.c.a	$2$	$3 \cdot 97$	$2$	4.0.873.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.292.4t3.a.a	$2$	$2^{2} \cdot 73$	$2$	4.0.1168.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.295.4t3.c.a	$2$	$5 \cdot 59$	$2$	4.2.1475.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.299.4t3.a.a	$2$	$13 \cdot 23$	$2$	4.2.3887.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.305.4t3.a.a	$2$	$5 \cdot 61$	$2$	4.0.1525.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$-2$
2.308.4t3.c.a	$2$	$2^{2} \cdot 7 \cdot 11$	$3$	4.0.2156.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.308.4t3.d.a	$2$	$2^{2} \cdot 7 \cdot 11$	$3$	4.0.2156.2	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.320.4t3.a.a	$2$	$2^{6} \cdot 5$	$2$	4.0.1280.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.323.4t3.a.a	$2$	$17 \cdot 19$	$2$	4.2.5491.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.327.4t3.c.a	$2$	$3 \cdot 109$	$2$	4.0.981.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.328.4t3.c.a	$2$	$2^{3} \cdot 41$	$2$	4.4.2624.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$2$
2.328.4t3.d.a	$2$	$2^{3} \cdot 41$	$2$	4.0.2624.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.336.4t3.a.a	$2$	$2^{4} \cdot 3 \cdot 7$	$3$	4.0.1008.1	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$
2.336.4t3.b.a	$2$	$2^{4} \cdot 3 \cdot 7$	$3$	4.0.1008.2	$D_{4}$	$C_2^2$	$D_{4}$	$1$	$0$

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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.