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Automorphic Representations of GSp(4)

Weight 12, conductor dividing 16

The following table gives a complete list of the Galois orbits of cuspidal automorphic representations ππv of GSp(4,AQ) with the following properties:
labellift fromsizep=2p=3 paramodular SiegelKlingen Borelprincipal
typeεLT(3) K(1)K(2)K(4)K(8)K(16) Γ0(2)Γ0(4)Γ0(2)Γ0(4) B(2)Γ(2)S6 types
G.4.12.0.a1IIIa+1+728T+220T288488 00124 2815 430[4,2]+[3,2,1]+[2,2,2]
G.8.12.0.a1IVa+1+29T14760 00012 0202 116[3,2,1]
G.8.12.0.b1XIa+1210T229032 00012 0102 010[4,1,1]
G.8.12.0.c2X+1+26(12±56)T+221T2504(65±646) 00024 0000 00
G.16.12.0.a1VII+112456 00001 0402 015[3,1,1,1]+[2,1,1,1,1]
G.16.12.0.b2IXa+172(819±6485) 00002 0601 0202[3,1,1,1]
G.16.12.0.c2XIa+1210T72(521±1285) 00002 0000 00
G.16.12.0.d2XIa+1+210T72(831±885) 00002 0000 00
G.16.12.0.e5X+129t12,aT+221T2α12,16,a 00005 0000 00
G.16.12.0.f8X+129t12,bT+221T2α12,16,b 00008 0000 00
G.16.12.0.g1IIa or X-1+2126T+221T2185616 00001 0000 00
P.1.12.0.a1.22.a.a1IIb+(1+288T+221T2)(1210T)(1211T)107352 11223 3724 415[6]+[4,2]+[2,2,2]
P.2.12.0.a2.22.a.a1Vb+(1+210T)(1210T)(1211T)307800 01122 1312 29[4,2]
P.4.12.0.a2.22.a.b1VIb+(1210T)2295512 00000 1300 15[2,2,2]
P.8.12.0.a4.22.a.a2XIa*+1210T24(11209±1122161) 00000 0000 00
P.8.12.0.b8.22.a.a2XIb+(1210T)(1211T)24(7645±8358549 00022 0000 00
P.16.12.0.a8.22.a.b3XIa*+1210T268451β1 00000 0000 00
P.16.12.0.b16.22.a.e2XIb+(1210T)(1211T)48(6019±4358549) 00002 0000 00
P.16.12.0.c16.22.a.f3XIb+(1210T)(1211T)203941+β1 00003 0000 00
dimS12(Γ) 1241245 734418 12120