3.1.3.4a2.3

Defining Polynomial: \( x^{3} + 2\cdot 3 x^{2} + 7\cdot 3 \)

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Summary table

e v(N) Character Order Description Count
2 2 2 principal series 1
3 4 3 supercuspidal unramified 1
3 4 3 principal series 1
3 6 3 principal series 3
3 6 3 supercuspidal unramified 3
3 10 3 supercuspidal unramified 9
3 10 3 principal series 9
4 2 4 supercuspidal unramified 1
6 4 6 principal series 1
6 4 6 supercuspidal unramified 1
6 6 6 supercuspidal unramified 3
6 6 6 principal series 3
6 10 6 principal series 9
6 10 6 supercuspidal unramified 9
12 3 6 supercuspidal ramified 2
12 7 6 supercuspidal ramified 6
12 9 6 supercuspidal ramified 18
12 11 6 supercuspidal ramified 27

Inertial Types

Name e v(N) Character Order Description
ps.2.2.1.1.a 2 2 2 principal series
ps.3.4.1.1.a 3 4 3 principal series
ps.6.4.1.1.a 6 4 6 principal series
ps.3.6.1.1.a 3 6 3 principal series
ps.3.6.1.1.b 3 6 3 principal series
ps.3.6.1.1.c 3 6 3 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.3.10.1.1.a 3 10 3 principal series
ps.3.10.1.1.b 3 10 3 principal series
ps.3.10.1.1.c 3 10 3 principal series
ps.3.10.1.1.d 3 10 3 principal series
ps.3.10.1.1.e 3 10 3 principal series
ps.3.10.1.1.f 3 10 3 principal series
ps.3.10.1.1.g 3 10 3 principal series
ps.3.10.1.1.h 3 10 3 principal series
ps.3.10.1.1.i 3 10 3 principal series
ps.6.10.1.1.a 6 10 6 principal series
ps.6.10.1.1.b 6 10 6 principal series
ps.6.10.1.1.c 6 10 6 principal series
ps.6.10.1.1.d 6 10 6 principal series
ps.6.10.1.1.e 6 10 6 principal series
ps.6.10.1.1.f 6 10 6 principal series
ps.6.10.1.1.g 6 10 6 principal series
ps.6.10.1.1.h 6 10 6 principal series
ps.6.10.1.1.i 6 10 6 principal series
scu.4.2.1.31.a 4 2 4 supercuspidal unramified
scu.3.4.1.31.a 3 4 3 supercuspidal unramified
scu.6.4.1.31.a 6 4 6 supercuspidal unramified
scu.3.6.1.31.a 3 6 3 supercuspidal unramified
scu.3.6.1.31.b 3 6 3 supercuspidal unramified
scu.3.6.1.31.c 3 6 3 supercuspidal unramified
scu.6.6.1.31.a 6 6 6 supercuspidal unramified
scu.6.6.1.31.b 6 6 6 supercuspidal unramified
scu.6.6.1.31.c 6 6 6 supercuspidal unramified
scu.3.10.1.31.a 3 10 3 supercuspidal unramified
scu.3.10.1.31.b 3 10 3 supercuspidal unramified
scu.3.10.1.31.c 3 10 3 supercuspidal unramified
scu.3.10.1.31.d 3 10 3 supercuspidal unramified
scu.3.10.1.31.e 3 10 3 supercuspidal unramified
scu.3.10.1.31.f 3 10 3 supercuspidal unramified
scu.3.10.1.31.g 3 10 3 supercuspidal unramified
scu.3.10.1.31.h 3 10 3 supercuspidal unramified
scu.3.10.1.31.i 3 10 3 supercuspidal unramified
scu.6.10.1.31.a 6 10 6 supercuspidal unramified
scu.6.10.1.31.b 6 10 6 supercuspidal unramified
scu.6.10.1.31.c 6 10 6 supercuspidal unramified
scu.6.10.1.31.d 6 10 6 supercuspidal unramified
scu.6.10.1.31.e 6 10 6 supercuspidal unramified
scu.6.10.1.31.f 6 10 6 supercuspidal unramified
scu.6.10.1.31.g 6 10 6 supercuspidal unramified
scu.6.10.1.31.h 6 10 6 supercuspidal unramified
scu.6.10.1.31.i 6 10 6 supercuspidal unramified
scr.12.3.1.1.a 12 3 6 supercuspidal ramified
scr.12.3.1.2.a 12 3 6 supercuspidal ramified
scr.12.7.1.1.a 12 7 6 supercuspidal ramified
scr.12.7.1.1.b 12 7 6 supercuspidal ramified
scr.12.7.1.1.c 12 7 6 supercuspidal ramified
scr.12.7.1.2.a 12 7 6 supercuspidal ramified
scr.12.7.1.2.b 12 7 6 supercuspidal ramified
scr.12.7.1.2.c 12 7 6 supercuspidal ramified
scr.12.9.1.1.a 12 9 6 supercuspidal ramified
scr.12.9.1.1.b 12 9 6 supercuspidal ramified
scr.12.9.1.1.c 12 9 6 supercuspidal ramified
scr.12.9.1.1.d 12 9 6 supercuspidal ramified
scr.12.9.1.1.e 12 9 6 supercuspidal ramified
scr.12.9.1.1.f 12 9 6 supercuspidal ramified
scr.12.9.1.1.g 12 9 6 supercuspidal ramified
scr.12.9.1.1.h 12 9 6 supercuspidal ramified
scr.12.9.1.1.i 12 9 6 supercuspidal ramified
scr.12.9.1.2.a 12 9 6 supercuspidal ramified
scr.12.9.1.2.b 12 9 6 supercuspidal ramified
scr.12.9.1.2.c 12 9 6 supercuspidal ramified
scr.12.9.1.2.d 12 9 6 supercuspidal ramified
scr.12.9.1.2.e 12 9 6 supercuspidal ramified
scr.12.9.1.2.f 12 9 6 supercuspidal ramified
scr.12.9.1.2.g 12 9 6 supercuspidal ramified
scr.12.9.1.2.h 12 9 6 supercuspidal ramified
scr.12.9.1.2.i 12 9 6 supercuspidal ramified
scr.12.11.1.2.a 12 11 6 supercuspidal ramified
scr.12.11.1.2.b 12 11 6 supercuspidal ramified
scr.12.11.1.2.c 12 11 6 supercuspidal ramified
scr.12.11.1.2.d 12 11 6 supercuspidal ramified
scr.12.11.1.2.e 12 11 6 supercuspidal ramified
scr.12.11.1.2.f 12 11 6 supercuspidal ramified
scr.12.11.1.2.g 12 11 6 supercuspidal ramified
scr.12.11.1.2.h 12 11 6 supercuspidal ramified
scr.12.11.1.2.i 12 11 6 supercuspidal ramified
scr.12.11.1.2.j 12 11 6 supercuspidal ramified
scr.12.11.1.2.k 12 11 6 supercuspidal ramified
scr.12.11.1.2.l 12 11 6 supercuspidal ramified
scr.12.11.1.2.m 12 11 6 supercuspidal ramified
scr.12.11.1.2.n 12 11 6 supercuspidal ramified
scr.12.11.1.2.o 12 11 6 supercuspidal ramified
scr.12.11.1.2.p 12 11 6 supercuspidal ramified
scr.12.11.1.2.q 12 11 6 supercuspidal ramified
scr.12.11.1.2.r 12 11 6 supercuspidal ramified
scr.12.11.1.2.s 12 11 6 supercuspidal ramified
scr.12.11.1.2.t 12 11 6 supercuspidal ramified
scr.12.11.1.2.u 12 11 6 supercuspidal ramified
scr.12.11.1.2.v 12 11 6 supercuspidal ramified
scr.12.11.1.2.w 12 11 6 supercuspidal ramified
scr.12.11.1.2.x 12 11 6 supercuspidal ramified
scr.12.11.1.2.y 12 11 6 supercuspidal ramified
scr.12.11.1.2.z 12 11 6 supercuspidal ramified
scr.12.11.1.2.z27 12 11 6 supercuspidal ramified
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