Properties

Label 1155.4
Level 1155
Weight 4
Dimension 89024
Nonzero newspaces 48
Sturm bound 368640
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(368640\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1155))\).

Total New Old
Modular forms 140160 90112 50048
Cusp forms 136320 89024 47296
Eisenstein series 3840 1088 2752

Trace form

\( 89024 q + 16 q^{2} - 28 q^{3} - 152 q^{4} - 24 q^{5} - 16 q^{6} - 268 q^{7} - 248 q^{8} - 252 q^{9} + O(q^{10}) \) \( 89024 q + 16 q^{2} - 28 q^{3} - 152 q^{4} - 24 q^{5} - 16 q^{6} - 268 q^{7} - 248 q^{8} - 252 q^{9} - 740 q^{10} - 512 q^{11} - 648 q^{12} + 128 q^{13} + 60 q^{14} + 818 q^{15} + 3608 q^{16} + 1312 q^{17} + 808 q^{18} - 624 q^{19} - 1556 q^{20} + 232 q^{21} - 5368 q^{22} - 3344 q^{23} - 6168 q^{24} - 3988 q^{25} - 4096 q^{26} + 896 q^{27} - 2536 q^{28} + 3744 q^{29} + 7254 q^{30} + 7016 q^{31} + 10776 q^{32} + 7486 q^{33} + 10512 q^{34} + 5184 q^{35} + 9068 q^{36} + 4488 q^{37} + 6896 q^{38} - 264 q^{39} - 4876 q^{40} - 10336 q^{41} - 2280 q^{42} - 10416 q^{43} - 20552 q^{44} - 6102 q^{45} - 18072 q^{46} - 6960 q^{47} - 16964 q^{48} - 6924 q^{49} + 620 q^{50} - 11584 q^{51} - 88 q^{52} + 5808 q^{53} - 15372 q^{54} + 12148 q^{55} - 1576 q^{56} + 6040 q^{57} + 10232 q^{58} - 3152 q^{59} + 10938 q^{60} + 4808 q^{61} - 7648 q^{62} + 1646 q^{63} + 6928 q^{64} + 1072 q^{65} + 12248 q^{66} + 13768 q^{67} + 11280 q^{68} + 13940 q^{69} + 41920 q^{70} + 37664 q^{71} + 24068 q^{72} + 37512 q^{73} + 42848 q^{74} + 3510 q^{75} + 52672 q^{76} + 25344 q^{77} + 3360 q^{78} - 5416 q^{79} + 11276 q^{80} + 14572 q^{81} - 25152 q^{82} - 18064 q^{83} + 4872 q^{84} - 31172 q^{85} - 34696 q^{86} - 24308 q^{87} - 97040 q^{88} - 43712 q^{89} - 19698 q^{90} - 56284 q^{91} - 127912 q^{92} - 40028 q^{93} - 60712 q^{94} - 25176 q^{95} - 24932 q^{96} + 12424 q^{97} - 25864 q^{98} + 5024 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1155))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1155.4.a \(\chi_{1155}(1, \cdot)\) 1155.4.a.a 1 1
1155.4.a.b 1
1155.4.a.c 1
1155.4.a.d 1
1155.4.a.e 1
1155.4.a.f 1
1155.4.a.g 3
1155.4.a.h 4
1155.4.a.i 4
1155.4.a.j 4
1155.4.a.k 6
1155.4.a.l 6
1155.4.a.m 6
1155.4.a.n 6
1155.4.a.o 7
1155.4.a.p 7
1155.4.a.q 8
1155.4.a.r 8
1155.4.a.s 8
1155.4.a.t 9
1155.4.a.u 9
1155.4.a.v 9
1155.4.a.w 10
1155.4.c \(\chi_{1155}(694, \cdot)\) n/a 184 1
1155.4.d \(\chi_{1155}(881, \cdot)\) n/a 320 1
1155.4.f \(\chi_{1155}(659, \cdot)\) n/a 432 1
1155.4.i \(\chi_{1155}(76, \cdot)\) n/a 192 1
1155.4.k \(\chi_{1155}(769, \cdot)\) n/a 288 1
1155.4.l \(\chi_{1155}(1121, \cdot)\) n/a 288 1
1155.4.n \(\chi_{1155}(419, \cdot)\) n/a 480 1
1155.4.q \(\chi_{1155}(331, \cdot)\) n/a 320 2
1155.4.s \(\chi_{1155}(617, \cdot)\) n/a 720 2
1155.4.t \(\chi_{1155}(692, \cdot)\) n/a 1136 2
1155.4.v \(\chi_{1155}(727, \cdot)\) n/a 480 2
1155.4.y \(\chi_{1155}(43, \cdot)\) n/a 432 2
1155.4.z \(\chi_{1155}(421, \cdot)\) n/a 576 4
1155.4.bb \(\chi_{1155}(296, \cdot)\) n/a 768 2
1155.4.bc \(\chi_{1155}(439, \cdot)\) n/a 576 2
1155.4.bg \(\chi_{1155}(89, \cdot)\) n/a 960 2
1155.4.bi \(\chi_{1155}(551, \cdot)\) n/a 640 2
1155.4.bj \(\chi_{1155}(529, \cdot)\) n/a 480 2
1155.4.bl \(\chi_{1155}(241, \cdot)\) n/a 384 2
1155.4.bo \(\chi_{1155}(494, \cdot)\) n/a 1136 2
1155.4.br \(\chi_{1155}(104, \cdot)\) n/a 2272 4
1155.4.bt \(\chi_{1155}(281, \cdot)\) n/a 1152 4
1155.4.bu \(\chi_{1155}(139, \cdot)\) n/a 1152 4
1155.4.bw \(\chi_{1155}(391, \cdot)\) n/a 768 4
1155.4.bz \(\chi_{1155}(29, \cdot)\) n/a 1728 4
1155.4.cb \(\chi_{1155}(146, \cdot)\) n/a 1536 4
1155.4.cc \(\chi_{1155}(64, \cdot)\) n/a 864 4
1155.4.ce \(\chi_{1155}(142, \cdot)\) n/a 1152 4
1155.4.ch \(\chi_{1155}(397, \cdot)\) n/a 960 4
1155.4.cj \(\chi_{1155}(362, \cdot)\) n/a 2272 4
1155.4.ck \(\chi_{1155}(23, \cdot)\) n/a 1920 4
1155.4.cm \(\chi_{1155}(16, \cdot)\) n/a 1536 8
1155.4.cn \(\chi_{1155}(127, \cdot)\) n/a 1728 8
1155.4.cq \(\chi_{1155}(97, \cdot)\) n/a 2304 8
1155.4.cs \(\chi_{1155}(62, \cdot)\) n/a 4544 8
1155.4.ct \(\chi_{1155}(92, \cdot)\) n/a 3456 8
1155.4.cv \(\chi_{1155}(74, \cdot)\) n/a 4544 8
1155.4.cy \(\chi_{1155}(61, \cdot)\) n/a 1536 8
1155.4.da \(\chi_{1155}(4, \cdot)\) n/a 2304 8
1155.4.db \(\chi_{1155}(26, \cdot)\) n/a 3072 8
1155.4.dd \(\chi_{1155}(59, \cdot)\) n/a 4544 8
1155.4.dh \(\chi_{1155}(19, \cdot)\) n/a 2304 8
1155.4.di \(\chi_{1155}(116, \cdot)\) n/a 3072 8
1155.4.dl \(\chi_{1155}(53, \cdot)\) n/a 9088 16
1155.4.dm \(\chi_{1155}(17, \cdot)\) n/a 9088 16
1155.4.do \(\chi_{1155}(82, \cdot)\) n/a 4608 16
1155.4.dr \(\chi_{1155}(172, \cdot)\) n/a 4608 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1155))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1155)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 2}\)