2.2.1.0a1.1

Defining Polynomial: \( x^{2} + x + 1 \)

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Summary table

e v(N) Character Order Description Count
2 4 2 principal series 3
2 6 2 principal series 4
3 2 3 principal series 1
4 6 4 principal series 4
4 6 4 supercuspidal unramified 4
4 8 4 supercuspidal unramified 8
4 8 4 principal series 8
6 4 6 principal series 3
6 6 6 principal series 4
8 5 4 supercuspidal ramified 4
8 5 4 exceptional, Q8 8
8 6 4 exceptional, Q8 16
8 6 4 supercuspidal ramified 4
8 8 4 supercuspidal ramified 24
24 3 4 exceptional, SL(2,3) 3
24 4 4 exceptional, SL(2,3) 9
24 6 4 exceptional, SL(2,3) 12
24 7 4 exceptional, SL(2,3) 48

Inertial Types

Name e v(N) Character Order Description
ps.3.2.1.1.a 3 2 3 principal series
ps.2.4.1.1.a 2 4 2 principal series
ps.2.4.1.1.b 2 4 2 principal series
ps.2.4.1.1.c 2 4 2 principal series
ps.6.4.1.1.a 6 4 6 principal series
ps.6.4.1.1.b 6 4 6 principal series
ps.6.4.1.1.c 6 4 6 principal series
ps.2.6.1.1.a 2 6 2 principal series
ps.2.6.1.1.b 2 6 2 principal series
ps.2.6.1.1.c 2 6 2 principal series
ps.2.6.1.1.d 2 6 2 principal series
ps.4.6.1.1.a 4 6 4 principal series
ps.4.6.1.1.b 4 6 4 principal series
ps.4.6.1.1.c 4 6 4 principal series
ps.4.6.1.1.d 4 6 4 principal series
ps.6.6.1.1.a 6 6 6 principal series
ps.6.6.1.1.b 6 6 6 principal series
ps.6.6.1.1.c 6 6 6 principal series
ps.6.6.1.1.d 6 6 6 principal series
ps.4.8.1.1.a 4 8 4 principal series
ps.4.8.1.1.b 4 8 4 principal series
ps.4.8.1.1.c 4 8 4 principal series
ps.4.8.1.1.d 4 8 4 principal series
ps.4.8.1.1.e 4 8 4 principal series
ps.4.8.1.1.f 4 8 4 principal series
ps.4.8.1.1.g 4 8 4 principal series
ps.4.8.1.1.h 4 8 4 principal series
scu.4.6.1.15.a 4 6 4 supercuspidal unramified
scu.4.6.1.15.b 4 6 4 supercuspidal unramified
scu.4.6.1.15.c 4 6 4 supercuspidal unramified
scu.4.6.1.15.d 4 6 4 supercuspidal unramified
scu.4.8.1.15.a 4 8 4 supercuspidal unramified
scu.4.8.1.15.b 4 8 4 supercuspidal unramified
scu.4.8.1.15.c 4 8 4 supercuspidal unramified
scu.4.8.1.15.d 4 8 4 supercuspidal unramified
scu.4.8.1.15.e 4 8 4 supercuspidal unramified
scu.4.8.1.15.f 4 8 4 supercuspidal unramified
scu.4.8.1.15.g 4 8 4 supercuspidal unramified
scu.4.8.1.15.h 4 8 4 supercuspidal unramified
scr.8.5.1.1_3_5.a 8 5 4 supercuspidal ramified
scr.8.5.1.1_4_6.a 8 5 4 supercuspidal ramified
scr.8.5.1.2_3_6.a 8 5 4 supercuspidal ramified
scr.8.5.1.2_4_5.a 8 5 4 supercuspidal ramified
scr.8.6.1.1_3_5.a 8 6 4 supercuspidal ramified
scr.8.6.1.1_4_6.a 8 6 4 supercuspidal ramified
scr.8.6.1.2_3_6.a 8 6 4 supercuspidal ramified
scr.8.6.1.2_4_5.a 8 6 4 supercuspidal ramified
scr.8.8.1.1_7_10.a 8 8 4 supercuspidal ramified
scr.8.8.1.1_7_10.b 8 8 4 supercuspidal ramified
scr.8.8.1.1_8_9.a 8 8 4 supercuspidal ramified
scr.8.8.1.1_8_9.b 8 8 4 supercuspidal ramified
scr.8.8.1.2_11_14.a 8 8 4 supercuspidal ramified
scr.8.8.1.2_11_14.b 8 8 4 supercuspidal ramified
scr.8.8.1.2_12_13.a 8 8 4 supercuspidal ramified
scr.8.8.1.2_12_13.b 8 8 4 supercuspidal ramified
scr.8.8.1.3_10_13.a 8 8 4 supercuspidal ramified
scr.8.8.1.3_10_13.b 8 8 4 supercuspidal ramified
scr.8.8.1.3_7_11.a 8 8 4 supercuspidal ramified
scr.8.8.1.3_7_11.b 8 8 4 supercuspidal ramified
scr.8.8.1.3_8_12.a 8 8 4 supercuspidal ramified
scr.8.8.1.3_8_12.b 8 8 4 supercuspidal ramified
scr.8.8.1.3_9_14.a 8 8 4 supercuspidal ramified
scr.8.8.1.3_9_14.b 8 8 4 supercuspidal ramified
scr.8.8.1.5_7_13.a 8 8 4 supercuspidal ramified
scr.8.8.1.5_7_13.b 8 8 4 supercuspidal ramified
scr.8.8.1.5_8_14.a 8 8 4 supercuspidal ramified
scr.8.8.1.5_8_14.b 8 8 4 supercuspidal ramified
scr.8.8.1.6_10_12.a 8 8 4 supercuspidal ramified
scr.8.8.1.6_10_12.b 8 8 4 supercuspidal ramified
scr.8.8.1.6_9_11.a 8 8 4 supercuspidal ramified
scr.8.8.1.6_9_11.b 8 8 4 supercuspidal ramified
ex.8.5.4.35_67_95.a 8 5 4 exceptional, Q8
ex.8.5.4.35_67_95.b 8 5 4 exceptional, Q8
ex.8.5.4.35_67_95.c 8 5 4 exceptional, Q8
ex.8.5.4.35_67_95.d 8 5 4 exceptional, Q8
ex.8.5.4.53_79_101.a 8 5 4 exceptional, Q8
ex.8.5.4.53_79_101.b 8 5 4 exceptional, Q8
ex.8.5.4.53_79_101.c 8 5 4 exceptional, Q8
ex.8.5.4.53_79_101.d 8 5 4 exceptional, Q8
ex.8.6.4.21_51_97.a 8 6 4 exceptional, Q8
ex.8.6.4.21_51_97.b 8 6 4 exceptional, Q8
ex.8.6.4.21_51_97.c 8 6 4 exceptional, Q8
ex.8.6.4.21_51_97.d 8 6 4 exceptional, Q8
ex.8.6.4.21_51_97.e 8 6 4 exceptional, Q8
ex.8.6.4.21_51_97.f 8 6 4 exceptional, Q8
ex.8.6.4.21_51_97.g 8 6 4 exceptional, Q8
ex.8.6.4.21_51_97.h 8 6 4 exceptional, Q8
ex.8.6.4.35_67_95.a 8 6 4 exceptional, Q8
ex.8.6.4.35_67_95.b 8 6 4 exceptional, Q8
ex.8.6.4.35_67_95.c 8 6 4 exceptional, Q8
ex.8.6.4.35_67_95.d 8 6 4 exceptional, Q8
ex.8.6.4.53_79_101.a 8 6 4 exceptional, Q8
ex.8.6.4.53_79_101.b 8 6 4 exceptional, Q8
ex.8.6.4.53_79_101.c 8 6 4 exceptional, Q8
ex.8.6.4.53_79_101.d 8 6 4 exceptional, Q8
ex.24.3.1.1_3_5.a 24 3 4 exceptional, SL(2,3)
ex.24.3.2.1_3_5.a 24 3 4 exceptional, SL(2,3)
ex.24.3.2.1_3_5.b 24 3 4 exceptional, SL(2,3)
ex.24.4.1.1_3_5.a 24 4 4 exceptional, SL(2,3)
ex.24.4.1.1_3_5.b 24 4 4 exceptional, SL(2,3)
ex.24.4.1.1_3_5.c 24 4 4 exceptional, SL(2,3)
ex.24.4.2.1_3_5.a 24 4 4 exceptional, SL(2,3)
ex.24.4.2.1_3_5.b 24 4 4 exceptional, SL(2,3)
ex.24.4.2.1_3_5.c 24 4 4 exceptional, SL(2,3)
ex.24.4.2.1_3_5.d 24 4 4 exceptional, SL(2,3)
ex.24.4.2.1_3_5.e 24 4 4 exceptional, SL(2,3)
ex.24.4.2.1_3_5.f 24 4 4 exceptional, SL(2,3)
ex.24.6.1.1_3_5.a 24 6 4 exceptional, SL(2,3)
ex.24.6.1.1_3_5.b 24 6 4 exceptional, SL(2,3)
ex.24.6.1.1_3_5.c 24 6 4 exceptional, SL(2,3)
ex.24.6.1.1_3_5.d 24 6 4 exceptional, SL(2,3)
ex.24.6.2.1_3_5.a 24 6 4 exceptional, SL(2,3)
ex.24.6.2.1_3_5.b 24 6 4 exceptional, SL(2,3)
ex.24.6.2.1_3_5.c 24 6 4 exceptional, SL(2,3)
ex.24.6.2.1_3_5.d 24 6 4 exceptional, SL(2,3)
ex.24.6.2.1_3_5.e 24 6 4 exceptional, SL(2,3)
ex.24.6.2.1_3_5.f 24 6 4 exceptional, SL(2,3)
ex.24.6.2.1_3_5.g 24 6 4 exceptional, SL(2,3)
ex.24.6.2.1_3_5.h 24 6 4 exceptional, SL(2,3)
ex.24.7.1.55_79_103.a 24 7 4 exceptional, SL(2,3)
ex.24.7.1.55_79_103.b 24 7 4 exceptional, SL(2,3)
ex.24.7.1.55_79_103.c 24 7 4 exceptional, SL(2,3)
ex.24.7.1.55_79_103.d 24 7 4 exceptional, SL(2,3)
ex.24.7.1.55_79_103.e 24 7 4 exceptional, SL(2,3)
ex.24.7.1.55_79_103.f 24 7 4 exceptional, SL(2,3)
ex.24.7.1.55_79_103.g 24 7 4 exceptional, SL(2,3)
ex.24.7.1.55_79_103.h 24 7 4 exceptional, SL(2,3)
ex.24.7.1.57_83_109.a 24 7 4 exceptional, SL(2,3)
ex.24.7.1.57_83_109.b 24 7 4 exceptional, SL(2,3)
ex.24.7.1.57_83_109.c 24 7 4 exceptional, SL(2,3)
ex.24.7.1.57_83_109.d 24 7 4 exceptional, SL(2,3)
ex.24.7.1.57_83_109.e 24 7 4 exceptional, SL(2,3)
ex.24.7.1.57_83_109.f 24 7 4 exceptional, SL(2,3)
ex.24.7.1.57_83_109.g 24 7 4 exceptional, SL(2,3)
ex.24.7.1.57_83_109.h 24 7 4 exceptional, SL(2,3)
ex.24.7.2.40_87_112.a 24 7 4 exceptional, SL(2,3)
ex.24.7.2.40_87_112.b 24 7 4 exceptional, SL(2,3)
ex.24.7.2.40_87_112.c 24 7 4 exceptional, SL(2,3)
ex.24.7.2.40_87_112.d 24 7 4 exceptional, SL(2,3)
ex.24.7.2.40_87_112.e 24 7 4 exceptional, SL(2,3)
ex.24.7.2.40_87_112.f 24 7 4 exceptional, SL(2,3)
ex.24.7.2.40_87_112.g 24 7 4 exceptional, SL(2,3)
ex.24.7.2.40_87_112.h 24 7 4 exceptional, SL(2,3)
ex.24.7.2.44_93_114.a 24 7 4 exceptional, SL(2,3)
ex.24.7.2.44_93_114.b 24 7 4 exceptional, SL(2,3)
ex.24.7.2.44_93_114.c 24 7 4 exceptional, SL(2,3)
ex.24.7.2.44_93_114.d 24 7 4 exceptional, SL(2,3)
ex.24.7.2.44_93_114.e 24 7 4 exceptional, SL(2,3)
ex.24.7.2.44_93_114.f 24 7 4 exceptional, SL(2,3)
ex.24.7.2.44_93_114.g 24 7 4 exceptional, SL(2,3)
ex.24.7.2.44_93_114.h 24 7 4 exceptional, SL(2,3)
ex.24.7.2.48_72_119.a 24 7 4 exceptional, SL(2,3)
ex.24.7.2.48_72_119.b 24 7 4 exceptional, SL(2,3)
ex.24.7.2.48_72_119.c 24 7 4 exceptional, SL(2,3)
ex.24.7.2.48_72_119.d 24 7 4 exceptional, SL(2,3)
ex.24.7.2.48_72_119.e 24 7 4 exceptional, SL(2,3)
ex.24.7.2.48_72_119.f 24 7 4 exceptional, SL(2,3)
ex.24.7.2.48_72_119.g 24 7 4 exceptional, SL(2,3)
ex.24.7.2.48_72_119.h 24 7 4 exceptional, SL(2,3)
ex.24.7.2.54_74_123.a 24 7 4 exceptional, SL(2,3)
ex.24.7.2.54_74_123.b 24 7 4 exceptional, SL(2,3)
ex.24.7.2.54_74_123.c 24 7 4 exceptional, SL(2,3)
ex.24.7.2.54_74_123.d 24 7 4 exceptional, SL(2,3)
ex.24.7.2.54_74_123.e 24 7 4 exceptional, SL(2,3)
ex.24.7.2.54_74_123.f 24 7 4 exceptional, SL(2,3)
ex.24.7.2.54_74_123.g 24 7 4 exceptional, SL(2,3)
ex.24.7.2.54_74_123.h 24 7 4 exceptional, SL(2,3)
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