2.1.2.3a1.2

Defining Polynomial: \( x^{2} + 5\cdot 2 \)

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Summary table

e v(N) Character Order Description Count
2 4 2 principal series 1
2 8 2 principal series 2
2 10 2 principal series 4
3 2 3 supercuspidal unramified 1
4 6 4 principal series 1
4 6 4 supercuspidal unramified 1
4 8 4 supercuspidal unramified 1
4 8 4 principal series 1
4 10 4 supercuspidal unramified 2
4 10 4 principal series 2
4 14 4 principal series 8
4 14 4 supercuspidal unramified 8
6 4 6 supercuspidal unramified 1
6 8 6 supercuspidal unramified 2
6 10 6 supercuspidal unramified 4
8 5 4 supercuspidal ramified 2
8 8 4 supercuspidal ramified 2
8 10 4 supercuspidal ramified 4
8 11 4 supercuspidal ramified 16
8 12 4 supercuspidal ramified 8
8 14 4 supercuspidal ramified 24
24 3 4 exceptional, SL(2,3) 1
24 4 4 exceptional, SL(2,3) 1
24 7 4 exceptional, SL(2,3) 4
24 8 4 exceptional, SL(2,3) 6
24 9 4 exceptional, SL(2,3) 8
24 10 4 exceptional, SL(2,3) 20
24 13 4 exceptional, SL(2,3) 32

Inertial Types

Name e v(N) Character Order Description
ps.2.4.1.1.a 2 4 2 principal series
ps.4.6.1.1.a 4 6 4 principal series
ps.2.8.1.1.a 2 8 2 principal series
ps.2.8.1.1.b 2 8 2 principal series
ps.4.8.1.1.a 4 8 4 principal series
ps.2.10.1.1.a 2 10 2 principal series
ps.2.10.1.1.b 2 10 2 principal series
ps.2.10.1.1.c 2 10 2 principal series
ps.2.10.1.1.d 2 10 2 principal series
ps.4.10.1.1.a 4 10 4 principal series
ps.4.10.1.1.b 4 10 4 principal series
ps.4.14.1.1.a 4 14 4 principal series
ps.4.14.1.1.b 4 14 4 principal series
ps.4.14.1.1.c 4 14 4 principal series
ps.4.14.1.1.d 4 14 4 principal series
ps.4.14.1.1.e 4 14 4 principal series
ps.4.14.1.1.f 4 14 4 principal series
ps.4.14.1.1.g 4 14 4 principal series
ps.4.14.1.1.h 4 14 4 principal series
scu.3.2.1.15.a 3 2 3 supercuspidal unramified
scu.6.4.1.15.a 6 4 6 supercuspidal unramified
scu.4.6.1.15.a 4 6 4 supercuspidal unramified
scu.4.8.1.15.a 4 8 4 supercuspidal unramified
scu.6.8.1.15.a 6 8 6 supercuspidal unramified
scu.6.8.1.15.b 6 8 6 supercuspidal unramified
scu.4.10.1.15.a 4 10 4 supercuspidal unramified
scu.4.10.1.15.b 4 10 4 supercuspidal unramified
scu.6.10.1.15.a 6 10 6 supercuspidal unramified
scu.6.10.1.15.b 6 10 6 supercuspidal unramified
scu.6.10.1.15.c 6 10 6 supercuspidal unramified
scu.6.10.1.15.d 6 10 6 supercuspidal unramified
scu.4.14.1.15.a 4 14 4 supercuspidal unramified
scu.4.14.1.15.b 4 14 4 supercuspidal unramified
scu.4.14.1.15.c 4 14 4 supercuspidal unramified
scu.4.14.1.15.d 4 14 4 supercuspidal unramified
scu.4.14.1.15.e 4 14 4 supercuspidal unramified
scu.4.14.1.15.f 4 14 4 supercuspidal unramified
scu.4.14.1.15.g 4 14 4 supercuspidal unramified
scu.4.14.1.15.h 4 14 4 supercuspidal unramified
scr.8.5.1.1.a 8 5 4 supercuspidal ramified
scr.8.5.1.2.a 8 5 4 supercuspidal ramified
scr.8.8.1.1.a 8 8 4 supercuspidal ramified
scr.8.8.1.2.a 8 8 4 supercuspidal ramified
scr.8.10.1.1.a 8 10 4 supercuspidal ramified
scr.8.10.1.1.b 8 10 4 supercuspidal ramified
scr.8.10.1.2.a 8 10 4 supercuspidal ramified
scr.8.10.1.2.b 8 10 4 supercuspidal ramified
scr.8.11.1.3.a 8 11 4 supercuspidal ramified
scr.8.11.1.3.b 8 11 4 supercuspidal ramified
scr.8.11.1.3.c 8 11 4 supercuspidal ramified
scr.8.11.1.3.d 8 11 4 supercuspidal ramified
scr.8.11.1.4.a 8 11 4 supercuspidal ramified
scr.8.11.1.4.b 8 11 4 supercuspidal ramified
scr.8.11.1.4.c 8 11 4 supercuspidal ramified
scr.8.11.1.4.d 8 11 4 supercuspidal ramified
scr.8.11.1.5.a 8 11 4 supercuspidal ramified
scr.8.11.1.5.b 8 11 4 supercuspidal ramified
scr.8.11.1.5.c 8 11 4 supercuspidal ramified
scr.8.11.1.5.d 8 11 4 supercuspidal ramified
scr.8.11.1.6.a 8 11 4 supercuspidal ramified
scr.8.11.1.6.b 8 11 4 supercuspidal ramified
scr.8.11.1.6.c 8 11 4 supercuspidal ramified
scr.8.11.1.6.d 8 11 4 supercuspidal ramified
scr.8.12.1.1.a 8 12 4 supercuspidal ramified
scr.8.12.1.1.b 8 12 4 supercuspidal ramified
scr.8.12.1.1.c 8 12 4 supercuspidal ramified
scr.8.12.1.1.d 8 12 4 supercuspidal ramified
scr.8.12.1.2.a 8 12 4 supercuspidal ramified
scr.8.12.1.2.b 8 12 4 supercuspidal ramified
scr.8.12.1.2.c 8 12 4 supercuspidal ramified
scr.8.12.1.2.d 8 12 4 supercuspidal ramified
scr.8.14.1.1.a 8 14 4 supercuspidal ramified
scr.8.14.1.1.b 8 14 4 supercuspidal ramified
scr.8.14.1.1.c 8 14 4 supercuspidal ramified
scr.8.14.1.1.d 8 14 4 supercuspidal ramified
scr.8.14.1.1.e 8 14 4 supercuspidal ramified
scr.8.14.1.1.f 8 14 4 supercuspidal ramified
scr.8.14.1.1.g 8 14 4 supercuspidal ramified
scr.8.14.1.1.h 8 14 4 supercuspidal ramified
scr.8.14.1.3.a 8 14 4 supercuspidal ramified
scr.8.14.1.3.b 8 14 4 supercuspidal ramified
scr.8.14.1.3.c 8 14 4 supercuspidal ramified
scr.8.14.1.3.d 8 14 4 supercuspidal ramified
scr.8.14.1.4.a 8 14 4 supercuspidal ramified
scr.8.14.1.4.b 8 14 4 supercuspidal ramified
scr.8.14.1.4.c 8 14 4 supercuspidal ramified
scr.8.14.1.4.d 8 14 4 supercuspidal ramified
scr.8.14.1.5.a 8 14 4 supercuspidal ramified
scr.8.14.1.5.b 8 14 4 supercuspidal ramified
scr.8.14.1.5.c 8 14 4 supercuspidal ramified
scr.8.14.1.5.d 8 14 4 supercuspidal ramified
scr.8.14.1.6.a 8 14 4 supercuspidal ramified
scr.8.14.1.6.b 8 14 4 supercuspidal ramified
scr.8.14.1.6.c 8 14 4 supercuspidal ramified
scr.8.14.1.6.d 8 14 4 supercuspidal ramified
ex.24.3.1.1_3_5.a 24 3 4 exceptional, SL(2,3)
ex.24.4.1.1_3_5.a 24 4 4 exceptional, SL(2,3)
ex.24.7.1.31_63_95.a 24 7 4 exceptional, SL(2,3)
ex.24.7.1.31_63_95.b 24 7 4 exceptional, SL(2,3)
ex.24.7.1.33_67_101.a 24 7 4 exceptional, SL(2,3)
ex.24.7.1.33_67_101.b 24 7 4 exceptional, SL(2,3)
ex.24.8.1.1_3_5.a 24 8 4 exceptional, SL(2,3)
ex.24.8.1.1_3_5.b 24 8 4 exceptional, SL(2,3)
ex.24.8.1.31_63_95.a 24 8 4 exceptional, SL(2,3)
ex.24.8.1.31_63_95.b 24 8 4 exceptional, SL(2,3)
ex.24.8.1.33_67_101.a 24 8 4 exceptional, SL(2,3)
ex.24.8.1.33_67_101.b 24 8 4 exceptional, SL(2,3)
ex.24.9.1.127_255_383.a 24 9 4 exceptional, SL(2,3)
ex.24.9.1.127_255_383.b 24 9 4 exceptional, SL(2,3)
ex.24.9.1.127_255_383.c 24 9 4 exceptional, SL(2,3)
ex.24.9.1.127_255_383.d 24 9 4 exceptional, SL(2,3)
ex.24.9.1.131_259_387.a 24 9 4 exceptional, SL(2,3)
ex.24.9.1.131_259_387.b 24 9 4 exceptional, SL(2,3)
ex.24.9.1.131_259_387.c 24 9 4 exceptional, SL(2,3)
ex.24.9.1.131_259_387.d 24 9 4 exceptional, SL(2,3)
ex.24.10.1.127_255_383.a 24 10 4 exceptional, SL(2,3)
ex.24.10.1.127_255_383.b 24 10 4 exceptional, SL(2,3)
ex.24.10.1.127_255_383.c 24 10 4 exceptional, SL(2,3)
ex.24.10.1.127_255_383.d 24 10 4 exceptional, SL(2,3)
ex.24.10.1.131_259_387.a 24 10 4 exceptional, SL(2,3)
ex.24.10.1.131_259_387.b 24 10 4 exceptional, SL(2,3)
ex.24.10.1.131_259_387.c 24 10 4 exceptional, SL(2,3)
ex.24.10.1.131_259_387.d 24 10 4 exceptional, SL(2,3)
ex.24.10.1.1_3_5.a 24 10 4 exceptional, SL(2,3)
ex.24.10.1.1_3_5.b 24 10 4 exceptional, SL(2,3)
ex.24.10.1.1_3_5.c 24 10 4 exceptional, SL(2,3)
ex.24.10.1.1_3_5.d 24 10 4 exceptional, SL(2,3)
ex.24.10.1.31_63_95.a 24 10 4 exceptional, SL(2,3)
ex.24.10.1.31_63_95.b 24 10 4 exceptional, SL(2,3)
ex.24.10.1.31_63_95.c 24 10 4 exceptional, SL(2,3)
ex.24.10.1.31_63_95.d 24 10 4 exceptional, SL(2,3)
ex.24.10.1.33_67_101.a 24 10 4 exceptional, SL(2,3)
ex.24.10.1.33_67_101.b 24 10 4 exceptional, SL(2,3)
ex.24.10.1.33_67_101.c 24 10 4 exceptional, SL(2,3)
ex.24.10.1.33_67_101.d 24 10 4 exceptional, SL(2,3)
ex.24.13.1.3607_5119_6655.a 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3607_5119_6655.b 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3607_5119_6655.c 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3607_5119_6655.d 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3607_5119_6655.e 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3607_5119_6655.f 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3607_5119_6655.g 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3607_5119_6655.h 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3647_5199_6727.a 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3647_5199_6727.b 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3647_5199_6727.c 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3647_5199_6727.d 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3647_5199_6727.e 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3647_5199_6727.f 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3647_5199_6727.g 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3647_5199_6727.h 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3735_5375_7045.a 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3735_5375_7045.b 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3735_5375_7045.c 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3735_5375_7045.d 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3735_5375_7045.e 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3735_5375_7045.f 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3735_5375_7045.g 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3735_5375_7045.h 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3777_5459_7111.a 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3777_5459_7111.b 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3777_5459_7111.c 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3777_5459_7111.d 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3777_5459_7111.e 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3777_5459_7111.f 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3777_5459_7111.g 24 13 4 exceptional, SL(2,3)
ex.24.13.1.3777_5459_7111.h 24 13 4 exceptional, SL(2,3)
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