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Properties

Label 3168.2
Level 3168
Weight 2
Dimension 120258
Nonzero newspaces 48
Sturm bound 1105920
Trace bound 49

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Defining parameters

Level: \( N \) = \( 3168 = 2^{5} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(1105920\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3168))\).

Total New Old
Modular forms 281600 121878 159722
Cusp forms 271361 120258 151103
Eisenstein series 10239 1620 8619

Trace form

\( 120258 q - 96 q^{2} - 96 q^{3} - 96 q^{4} - 92 q^{5} - 128 q^{6} - 70 q^{7} - 96 q^{8} - 192 q^{9} + O(q^{10}) \) \( 120258 q - 96 q^{2} - 96 q^{3} - 96 q^{4} - 92 q^{5} - 128 q^{6} - 70 q^{7} - 96 q^{8} - 192 q^{9} - 304 q^{10} - 84 q^{11} - 288 q^{12} - 108 q^{13} - 128 q^{14} - 108 q^{15} - 136 q^{16} - 88 q^{17} - 128 q^{18} - 246 q^{19} - 128 q^{20} - 160 q^{21} - 120 q^{22} - 216 q^{23} - 128 q^{24} - 210 q^{25} - 56 q^{26} - 120 q^{27} - 248 q^{28} - 140 q^{29} - 96 q^{30} - 142 q^{31} - 56 q^{32} - 356 q^{33} - 192 q^{34} - 114 q^{35} - 80 q^{36} - 220 q^{37} + 112 q^{38} - 84 q^{39} + 136 q^{40} - 40 q^{41} + 32 q^{42} - 32 q^{43} + 28 q^{44} - 192 q^{45} - 96 q^{46} + 42 q^{47} + 80 q^{48} + 90 q^{49} + 240 q^{50} - 32 q^{51} + 144 q^{52} + 36 q^{53} + 48 q^{54} - 198 q^{55} + 80 q^{56} - 96 q^{57} + 168 q^{58} + 58 q^{59} - 16 q^{60} - 108 q^{61} - 24 q^{62} + 12 q^{63} - 216 q^{64} - 76 q^{65} - 144 q^{66} - 112 q^{67} - 8 q^{68} - 72 q^{70} + 26 q^{71} - 128 q^{72} - 600 q^{73} - 128 q^{74} + 128 q^{75} - 96 q^{76} - 172 q^{77} - 336 q^{78} - 50 q^{79} - 344 q^{80} + 96 q^{81} - 608 q^{82} + 182 q^{83} - 352 q^{84} - 320 q^{85} - 472 q^{86} + 220 q^{87} - 272 q^{88} - 284 q^{89} - 416 q^{90} - 6 q^{91} - 632 q^{92} - 128 q^{93} - 440 q^{94} + 306 q^{95} - 400 q^{96} - 272 q^{97} - 536 q^{98} + 34 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3168))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3168.2.a \(\chi_{3168}(1, \cdot)\) 3168.2.a.a 1 1
3168.2.a.b 1
3168.2.a.c 1
3168.2.a.d 1
3168.2.a.e 1
3168.2.a.f 1
3168.2.a.g 1
3168.2.a.h 1
3168.2.a.i 1
3168.2.a.j 1
3168.2.a.k 1
3168.2.a.l 1
3168.2.a.m 1
3168.2.a.n 1
3168.2.a.o 1
3168.2.a.p 1
3168.2.a.q 1
3168.2.a.r 1
3168.2.a.s 1
3168.2.a.t 1
3168.2.a.u 1
3168.2.a.v 1
3168.2.a.w 1
3168.2.a.x 1
3168.2.a.y 1
3168.2.a.z 1
3168.2.a.ba 1
3168.2.a.bb 1
3168.2.a.bc 2
3168.2.a.bd 2
3168.2.a.be 2
3168.2.a.bf 2
3168.2.a.bg 3
3168.2.a.bh 3
3168.2.a.bi 4
3168.2.a.bj 4
3168.2.b \(\chi_{3168}(2177, \cdot)\) 3168.2.b.a 2 1
3168.2.b.b 2
3168.2.b.c 2
3168.2.b.d 2
3168.2.b.e 2
3168.2.b.f 2
3168.2.b.g 2
3168.2.b.h 2
3168.2.b.i 4
3168.2.b.j 4
3168.2.b.k 4
3168.2.b.l 4
3168.2.b.m 8
3168.2.b.n 8
3168.2.d \(\chi_{3168}(287, \cdot)\) 3168.2.d.a 8 1
3168.2.d.b 8
3168.2.d.c 12
3168.2.d.d 12
3168.2.f \(\chi_{3168}(1585, \cdot)\) 3168.2.f.a 2 1
3168.2.f.b 2
3168.2.f.c 2
3168.2.f.d 4
3168.2.f.e 4
3168.2.f.f 6
3168.2.f.g 10
3168.2.f.h 20
3168.2.h \(\chi_{3168}(2287, \cdot)\) 3168.2.h.a 2 1
3168.2.h.b 2
3168.2.h.c 2
3168.2.h.d 4
3168.2.h.e 4
3168.2.h.f 8
3168.2.h.g 8
3168.2.h.h 12
3168.2.h.i 16
3168.2.k \(\chi_{3168}(1871, \cdot)\) 3168.2.k.a 40 1
3168.2.m \(\chi_{3168}(593, \cdot)\) 3168.2.m.a 4 1
3168.2.m.b 4
3168.2.m.c 40
3168.2.o \(\chi_{3168}(703, \cdot)\) 3168.2.o.a 4 1
3168.2.o.b 4
3168.2.o.c 4
3168.2.o.d 12
3168.2.o.e 12
3168.2.o.f 24
3168.2.q \(\chi_{3168}(1057, \cdot)\) n/a 240 2
3168.2.r \(\chi_{3168}(1495, \cdot)\) None 0 2
3168.2.u \(\chi_{3168}(793, \cdot)\) None 0 2
3168.2.v \(\chi_{3168}(1079, \cdot)\) None 0 2
3168.2.y \(\chi_{3168}(1385, \cdot)\) None 0 2
3168.2.z \(\chi_{3168}(289, \cdot)\) n/a 240 4
3168.2.bc \(\chi_{3168}(1759, \cdot)\) n/a 288 2
3168.2.be \(\chi_{3168}(1649, \cdot)\) n/a 280 2
3168.2.bg \(\chi_{3168}(815, \cdot)\) n/a 240 2
3168.2.bh \(\chi_{3168}(175, \cdot)\) n/a 280 2
3168.2.bj \(\chi_{3168}(529, \cdot)\) n/a 240 2
3168.2.bl \(\chi_{3168}(1343, \cdot)\) n/a 240 2
3168.2.bn \(\chi_{3168}(65, \cdot)\) n/a 288 2
3168.2.br \(\chi_{3168}(397, \cdot)\) n/a 800 4
3168.2.bs \(\chi_{3168}(197, \cdot)\) n/a 768 4
3168.2.bt \(\chi_{3168}(683, \cdot)\) n/a 640 4
3168.2.bu \(\chi_{3168}(307, \cdot)\) n/a 952 4
3168.2.by \(\chi_{3168}(127, \cdot)\) n/a 240 4
3168.2.ca \(\chi_{3168}(17, \cdot)\) n/a 192 4
3168.2.cc \(\chi_{3168}(719, \cdot)\) n/a 192 4
3168.2.cf \(\chi_{3168}(271, \cdot)\) n/a 232 4
3168.2.ch \(\chi_{3168}(433, \cdot)\) n/a 232 4
3168.2.cj \(\chi_{3168}(575, \cdot)\) n/a 192 4
3168.2.cl \(\chi_{3168}(161, \cdot)\) n/a 192 4
3168.2.cn \(\chi_{3168}(23, \cdot)\) None 0 4
3168.2.co \(\chi_{3168}(329, \cdot)\) None 0 4
3168.2.cr \(\chi_{3168}(439, \cdot)\) None 0 4
3168.2.cs \(\chi_{3168}(265, \cdot)\) None 0 4
3168.2.cu \(\chi_{3168}(97, \cdot)\) n/a 1152 8
3168.2.cv \(\chi_{3168}(233, \cdot)\) None 0 8
3168.2.cy \(\chi_{3168}(71, \cdot)\) None 0 8
3168.2.cz \(\chi_{3168}(361, \cdot)\) None 0 8
3168.2.dc \(\chi_{3168}(343, \cdot)\) None 0 8
3168.2.dd \(\chi_{3168}(461, \cdot)\) n/a 4576 8
3168.2.de \(\chi_{3168}(133, \cdot)\) n/a 3840 8
3168.2.dj \(\chi_{3168}(43, \cdot)\) n/a 4576 8
3168.2.dk \(\chi_{3168}(155, \cdot)\) n/a 3840 8
3168.2.dm \(\chi_{3168}(545, \cdot)\) n/a 1152 8
3168.2.do \(\chi_{3168}(191, \cdot)\) n/a 1152 8
3168.2.dq \(\chi_{3168}(49, \cdot)\) n/a 1120 8
3168.2.ds \(\chi_{3168}(79, \cdot)\) n/a 1120 8
3168.2.dt \(\chi_{3168}(47, \cdot)\) n/a 1120 8
3168.2.dv \(\chi_{3168}(497, \cdot)\) n/a 1120 8
3168.2.dx \(\chi_{3168}(607, \cdot)\) n/a 1152 8
3168.2.ec \(\chi_{3168}(19, \cdot)\) n/a 3808 16
3168.2.ed \(\chi_{3168}(179, \cdot)\) n/a 3072 16
3168.2.ee \(\chi_{3168}(413, \cdot)\) n/a 3072 16
3168.2.ef \(\chi_{3168}(37, \cdot)\) n/a 3808 16
3168.2.ej \(\chi_{3168}(25, \cdot)\) None 0 16
3168.2.ek \(\chi_{3168}(7, \cdot)\) None 0 16
3168.2.en \(\chi_{3168}(41, \cdot)\) None 0 16
3168.2.eo \(\chi_{3168}(119, \cdot)\) None 0 16
3168.2.eq \(\chi_{3168}(59, \cdot)\) n/a 18304 32
3168.2.er \(\chi_{3168}(139, \cdot)\) n/a 18304 32
3168.2.ew \(\chi_{3168}(157, \cdot)\) n/a 18304 32
3168.2.ex \(\chi_{3168}(29, \cdot)\) n/a 18304 32

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3168))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3168)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1056))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3168))\)\(^{\oplus 1}\)