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Properties

Label 1168.3
Level 1168
Weight 3
Dimension 47614
Nonzero newspaces 30
Sturm bound 255744
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1168 = 2^{4} \cdot 73 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(255744\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1168))\).

Total New Old
Modular forms 86256 48254 38002
Cusp forms 84240 47614 36626
Eisenstein series 2016 640 1376

Trace form

\( 47614 q - 140 q^{2} - 104 q^{3} - 128 q^{4} - 164 q^{5} - 128 q^{6} - 100 q^{7} - 152 q^{8} - 54 q^{9} + O(q^{10}) \) \( 47614 q - 140 q^{2} - 104 q^{3} - 128 q^{4} - 164 q^{5} - 128 q^{6} - 100 q^{7} - 152 q^{8} - 54 q^{9} - 216 q^{10} - 72 q^{11} - 248 q^{12} - 196 q^{13} - 168 q^{14} - 108 q^{15} - 64 q^{16} - 256 q^{17} + 4 q^{18} - 168 q^{19} + 24 q^{20} - 140 q^{21} - 40 q^{22} - 228 q^{23} - 240 q^{24} - 58 q^{25} - 336 q^{26} - 236 q^{27} - 256 q^{28} - 228 q^{29} - 248 q^{30} - 108 q^{31} - 160 q^{32} - 316 q^{33} + 8 q^{34} + 92 q^{35} - 40 q^{36} - 132 q^{37} - 224 q^{38} + 284 q^{39} - 224 q^{40} - 72 q^{41} - 96 q^{42} + 120 q^{43} - 184 q^{44} - 204 q^{45} - 200 q^{46} - 108 q^{47} - 96 q^{48} - 330 q^{49} - 236 q^{50} - 420 q^{51} - 344 q^{52} - 516 q^{53} - 208 q^{54} - 612 q^{55} + 192 q^{56} - 36 q^{57} + 208 q^{58} - 520 q^{59} + 176 q^{60} - 196 q^{61} + 144 q^{62} - 108 q^{63} - 272 q^{64} - 228 q^{65} - 536 q^{66} + 344 q^{67} - 368 q^{68} + 52 q^{69} - 112 q^{70} + 412 q^{71} - 248 q^{72} + 74 q^{73} - 104 q^{74} + 368 q^{75} + 232 q^{76} + 244 q^{77} + 24 q^{78} - 108 q^{79} - 608 q^{80} - 658 q^{81} - 752 q^{82} - 744 q^{83} - 608 q^{84} - 116 q^{85} - 680 q^{86} - 996 q^{87} - 128 q^{88} + 120 q^{89} + 176 q^{90} - 484 q^{91} + 192 q^{92} - 116 q^{93} - 240 q^{94} - 108 q^{95} + 16 q^{96} - 576 q^{97} - 164 q^{98} + 344 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1168))\)

We only show spaces with odd 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
1168.3.c \(\chi_{1168}(1167, \cdot)\) 1168.3.c.a 2 1
1168.3.c.b 2
1168.3.c.c 2
1168.3.c.d 20
1168.3.c.e 48
1168.3.d \(\chi_{1168}(1023, \cdot)\) 1168.3.d.a 24 1
1168.3.d.b 48
1168.3.g \(\chi_{1168}(439, \cdot)\) None 0 1
1168.3.h \(\chi_{1168}(583, \cdot)\) None 0 1
1168.3.k \(\chi_{1168}(119, \cdot)\) None 0 2
1168.3.l \(\chi_{1168}(27, \cdot)\) n/a 588 2
1168.3.n \(\chi_{1168}(291, \cdot)\) n/a 588 2
1168.3.q \(\chi_{1168}(147, \cdot)\) n/a 576 2
1168.3.s \(\chi_{1168}(411, \cdot)\) n/a 588 2
1168.3.u \(\chi_{1168}(319, \cdot)\) n/a 148 2
1168.3.w \(\chi_{1168}(575, \cdot)\) n/a 148 2
1168.3.x \(\chi_{1168}(447, \cdot)\) n/a 148 2
1168.3.z \(\chi_{1168}(503, \cdot)\) None 0 2
1168.3.ba \(\chi_{1168}(519, \cdot)\) None 0 2
1168.3.bc \(\chi_{1168}(229, \cdot)\) n/a 1176 4
1168.3.bf \(\chi_{1168}(489, \cdot)\) None 0 4
1168.3.bh \(\chi_{1168}(209, \cdot)\) n/a 292 4
1168.3.bi \(\chi_{1168}(197, \cdot)\) n/a 1176 4
1168.3.bl \(\chi_{1168}(295, \cdot)\) None 0 4
1168.3.bn \(\chi_{1168}(195, \cdot)\) n/a 1176 4
1168.3.bp \(\chi_{1168}(155, \cdot)\) n/a 1176 4
1168.3.bs \(\chi_{1168}(227, \cdot)\) n/a 1176 4
1168.3.bu \(\chi_{1168}(3, \cdot)\) n/a 1176 4
1168.3.bv \(\chi_{1168}(143, \cdot)\) n/a 296 4
1168.3.bx \(\chi_{1168}(71, \cdot)\) None 0 6
1168.3.by \(\chi_{1168}(55, \cdot)\) None 0 6
1168.3.cb \(\chi_{1168}(255, \cdot)\) n/a 444 6
1168.3.cc \(\chi_{1168}(223, \cdot)\) n/a 444 6
1168.3.cf \(\chi_{1168}(125, \cdot)\) n/a 2352 8
1168.3.cg \(\chi_{1168}(17, \cdot)\) n/a 584 8
1168.3.ci \(\chi_{1168}(153, \cdot)\) None 0 8
1168.3.cl \(\chi_{1168}(21, \cdot)\) n/a 2352 8
1168.3.cn \(\chi_{1168}(79, \cdot)\) n/a 888 12
1168.3.co \(\chi_{1168}(75, \cdot)\) n/a 3528 12
1168.3.cr \(\chi_{1168}(19, \cdot)\) n/a 3528 12
1168.3.cs \(\chi_{1168}(35, \cdot)\) n/a 3528 12
1168.3.cv \(\chi_{1168}(91, \cdot)\) n/a 3528 12
1168.3.cx \(\chi_{1168}(23, \cdot)\) None 0 12
1168.3.cz \(\chi_{1168}(45, \cdot)\) n/a 7056 24
1168.3.da \(\chi_{1168}(185, \cdot)\) None 0 24
1168.3.dd \(\chi_{1168}(33, \cdot)\) n/a 1752 24
1168.3.de \(\chi_{1168}(5, \cdot)\) n/a 7056 24

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1168))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1168)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(73))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(146))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(292))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1168))\)\(^{\oplus 1}\)