Artin Representation Search Results

Dimension	Conductor	Group	Root number	Parity
Smallest container	Ramified primes	Unramified primes	Frobenius-Schur indicator

Results (displaying all 28 matches)

Galois conjugate representations are grouped into single lines.

Label	Dimension	Conductor	Defining polynomial of Artin field	$G$	Ind	$\chi(c)$
6.2e6_7e2_73e2.7t6.1c1	$6$	$ 2^{6} \cdot 7^{2} \cdot 73^{2}$	x^7 - 2x^6 + 2x^4 - 2x^3 - 2x^2 + 2x + 2	$A_7$	$1$	$2$
6.2e6_3e8_11e2.7t6.1c1	$6$	$ 2^{6} \cdot 3^{8} \cdot 11^{2}$	x^7 - 2x^6 + 2x + 2	$A_7$	$1$	$2$
6.2e6_3e6_7e4.7t6.1c1	$6$	$ 2^{6} \cdot 3^{6} \cdot 7^{4}$	x^7 - 3x^6 + 3x^5 + 3x^4 - 9x^3 + 3x^2 + x - 3	$A_7$	$1$	$2$
6.149e2_211e2.7t6.1c1	$6$	$ 149^{2} \cdot 211^{2}$	x^7 - 2x^6 - 7x^5 + 11x^4 + 16x^3 - 14x^2 - 11x + 2	$A_7$	$1$	$6$
10.2e9_3e14_7e8.70.1c1 10.2e9_3e14_7e8.70.1c2	$10$	$ 2^{9} \cdot 3^{14} \cdot 7^{8}$	x^7 - 3x^6 + 3x^5 + 3x^4 - 9x^3 + 3x^2 + x - 3	$A_7$	$0$	$-2$
10.2e9_3e18_11e6.70.1c1 10.2e9_3e18_11e6.70.1c2	$10$	$ 2^{9} \cdot 3^{18} \cdot 11^{6}$	x^7 - 2x^6 + 2x + 2	$A_7$	$0$	$-2$
10.2e9_7e6_73e6.70.1c1 10.2e9_7e6_73e6.70.1c2	$10$	$ 2^{9} \cdot 7^{6} \cdot 73^{6}$	x^7 - 2x^6 + 2x^4 - 2x^3 - 2x^2 + 2x + 2	$A_7$	$0$	$-2$
10.149e6_211e6.70.1c1 10.149e6_211e6.70.1c2	$10$	$ 149^{6} \cdot 211^{6}$	x^7 - 2x^6 - 7x^5 + 11x^4 + 16x^3 - 14x^2 - 11x + 2	$A_7$	$0$	$10$
14.2e12_3e18_7e12.15t47.1c1	$14$	$ 2^{12} \cdot 3^{18} \cdot 7^{12}$	x^7 - 3x^6 + 3x^5 + 3x^4 - 9x^3 + 3x^2 + x - 3	$A_7$	$1$	$2$
14.2e12_3e18_7e12.21t33.1c1	$14$	$ 2^{12} \cdot 3^{18} \cdot 7^{12}$	x^7 - 3x^6 + 3x^5 + 3x^4 - 9x^3 + 3x^2 + x - 3	$A_7$	$1$	$2$
14.2e12_3e24_11e8.21t33.1c1	$14$	$ 2^{12} \cdot 3^{24} \cdot 11^{8}$	x^7 - 2x^6 + 2x + 2	$A_7$	$1$	$2$
14.2e12_7e6_73e8.21t33.1c1	$14$	$ 2^{12} \cdot 7^{6} \cdot 73^{8}$	x^7 - 2x^6 + 2x^4 - 2x^3 - 2x^2 + 2x + 2	$A_7$	$1$	$2$
14.2e12_7e6_73e10.15t47.1c1	$14$	$ 2^{12} \cdot 7^{6} \cdot 73^{10}$	x^7 - 2x^6 + 2x^4 - 2x^3 - 2x^2 + 2x + 2	$A_7$	$1$	$2$
14.2e12_3e28_11e10.15t47.1c1	$14$	$ 2^{12} \cdot 3^{28} \cdot 11^{10}$	x^7 - 2x^6 + 2x + 2	$A_7$	$1$	$2$
14.149e8_211e8.21t33.1c1	$14$	$ 149^{8} \cdot 211^{8}$	x^7 - 2x^6 - 7x^5 + 11x^4 + 16x^3 - 14x^2 - 11x + 2	$A_7$	$1$	$14$
14.149e10_211e10.15t47.1c1	$14$	$ 149^{10} \cdot 211^{10}$	x^7 - 2x^6 - 7x^5 + 11x^4 + 16x^3 - 14x^2 - 11x + 2	$A_7$	$1$	$14$
15.2e12_3e20_7e12.42t294.1c1	$15$	$ 2^{12} \cdot 3^{20} \cdot 7^{12}$	x^7 - 3x^6 + 3x^5 + 3x^4 - 9x^3 + 3x^2 + x - 3	$A_7$	$1$	$-1$
15.2e12_3e26_11e8.42t294.1c1	$15$	$ 2^{12} \cdot 3^{26} \cdot 11^{8}$	x^7 - 2x^6 + 2x + 2	$A_7$	$1$	$-1$
15.2e12_7e8_73e8.42t294.1c1	$15$	$ 2^{12} \cdot 7^{8} \cdot 73^{8}$	x^7 - 2x^6 + 2x^4 - 2x^3 - 2x^2 + 2x + 2	$A_7$	$1$	$-1$
15.149e8_211e8.42t294.1c1	$15$	$ 149^{8} \cdot 211^{8}$	x^7 - 2x^6 - 7x^5 + 11x^4 + 16x^3 - 14x^2 - 11x + 2	$A_7$	$1$	$15$
21.2e18_3e30_7e16.42t299.1c1	$21$	$ 2^{18} \cdot 3^{30} \cdot 7^{16}$	x^7 - 3x^6 + 3x^5 + 3x^4 - 9x^3 + 3x^2 + x - 3	$A_7$	$1$	$1$
21.2e18_3e44_11e16.42t299.1c1	$21$	$ 2^{18} \cdot 3^{44} \cdot 11^{16}$	x^7 - 2x^6 + 2x + 2	$A_7$	$1$	$1$
21.2e18_7e10_73e16.42t299.1c1	$21$	$ 2^{18} \cdot 7^{10} \cdot 73^{16}$	x^7 - 2x^6 + 2x^4 - 2x^3 - 2x^2 + 2x + 2	$A_7$	$1$	$1$
21.149e16_211e16.42t299.1c1	$21$	$ 149^{16} \cdot 211^{16}$	x^7 - 2x^6 - 7x^5 + 11x^4 + 16x^3 - 14x^2 - 11x + 2	$A_7$	$1$	$21$
35.2e30_3e50_7e28.70.1c1	$35$	$ 2^{30} \cdot 3^{50} \cdot 7^{28}$	x^7 - 3x^6 + 3x^5 + 3x^4 - 9x^3 + 3x^2 + x - 3	$A_7$	$1$	$-1$
35.2e30_3e68_11e24.70.1c1	$35$	$ 2^{30} \cdot 3^{68} \cdot 11^{24}$	x^7 - 2x^6 + 2x + 2	$A_7$	$1$	$-1$
35.2e30_7e18_73e24.70.1c1	$35$	$ 2^{30} \cdot 7^{18} \cdot 73^{24}$	x^7 - 2x^6 + 2x^4 - 2x^3 - 2x^2 + 2x + 2	$A_7$	$1$	$-1$
35.149e24_211e24.70.1c1	$35$	$ 149^{24} \cdot 211^{24}$	x^7 - 2x^6 - 7x^5 + 11x^4 + 16x^3 - 14x^2 - 11x + 2	$A_7$	$1$	$35$