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Properties

Label 2268.4
Level 2268
Weight 4
Dimension 184912
Nonzero newspaces 44
Sturm bound 1119744
Trace bound 26

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Defining parameters

Level: \( N \) = \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 44 \)
Sturm bound: \(1119744\)
Trace bound: \(26\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2268))\).

Total New Old
Modular forms 423144 186032 237112
Cusp forms 416664 184912 231752
Eisenstein series 6480 1120 5360

Trace form

\( 184912 q - 48 q^{2} - 80 q^{4} - 72 q^{5} - 72 q^{6} - 18 q^{7} - 126 q^{8} - 144 q^{9} + O(q^{10}) \) \( 184912 q - 48 q^{2} - 80 q^{4} - 72 q^{5} - 72 q^{6} - 18 q^{7} - 126 q^{8} - 144 q^{9} - 148 q^{10} - 174 q^{11} - 72 q^{12} - 124 q^{13} + 15 q^{14} + 280 q^{16} + 300 q^{17} - 72 q^{18} - 540 q^{19} + 414 q^{20} - 288 q^{21} - 240 q^{22} + 948 q^{23} - 72 q^{24} - 120 q^{25} - 18 q^{26} + 1404 q^{27} - 21 q^{28} + 1308 q^{29} - 72 q^{30} + 432 q^{31} - 1428 q^{32} - 1008 q^{33} - 1156 q^{34} - 1236 q^{35} - 180 q^{36} - 916 q^{37} - 1836 q^{38} + 1130 q^{40} + 5646 q^{41} + 3465 q^{42} + 1134 q^{43} + 10602 q^{44} + 1908 q^{45} + 2148 q^{46} - 4284 q^{47} - 4626 q^{48} - 3674 q^{49} - 15360 q^{50} - 5922 q^{51} - 6250 q^{52} - 10416 q^{53} - 13428 q^{54} - 6264 q^{55} - 8901 q^{56} - 4788 q^{57} - 1606 q^{58} - 834 q^{59} - 2646 q^{60} + 2720 q^{61} + 7488 q^{62} + 1998 q^{63} + 7378 q^{64} + 25812 q^{65} + 14760 q^{66} + 2646 q^{67} + 18516 q^{68} + 14076 q^{69} - 489 q^{70} + 480 q^{71} - 72 q^{72} - 5704 q^{73} - 11802 q^{74} - 9000 q^{75} - 6204 q^{76} - 15408 q^{77} - 666 q^{78} + 3276 q^{79} - 72 q^{80} - 11664 q^{81} + 3620 q^{82} - 1728 q^{83} + 153 q^{84} + 13972 q^{85} + 16608 q^{86} - 10944 q^{87} + 3840 q^{88} + 27660 q^{89} - 25146 q^{90} + 5634 q^{91} - 30558 q^{92} + 36756 q^{93} - 4530 q^{94} + 20712 q^{95} - 5922 q^{96} - 7378 q^{97} + 5751 q^{98} + 15084 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2268))\)

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
2268.4.a \(\chi_{2268}(1, \cdot)\) 2268.4.a.a 5 1
2268.4.a.b 5
2268.4.a.c 5
2268.4.a.d 5
2268.4.a.e 8
2268.4.a.f 8
2268.4.a.g 9
2268.4.a.h 9
2268.4.a.i 9
2268.4.a.j 9
2268.4.b \(\chi_{2268}(811, \cdot)\) n/a 568 1
2268.4.e \(\chi_{2268}(323, \cdot)\) n/a 432 1
2268.4.f \(\chi_{2268}(1133, \cdot)\) 2268.4.f.a 48 1
2268.4.f.b 48
2268.4.i \(\chi_{2268}(865, \cdot)\) n/a 192 2
2268.4.j \(\chi_{2268}(757, \cdot)\) n/a 144 2
2268.4.k \(\chi_{2268}(1297, \cdot)\) n/a 192 2
2268.4.l \(\chi_{2268}(109, \cdot)\) n/a 192 2
2268.4.n \(\chi_{2268}(1027, \cdot)\) n/a 1144 2
2268.4.o \(\chi_{2268}(107, \cdot)\) n/a 1144 2
2268.4.t \(\chi_{2268}(1781, \cdot)\) n/a 192 2
2268.4.w \(\chi_{2268}(269, \cdot)\) n/a 192 2
2268.4.x \(\chi_{2268}(377, \cdot)\) n/a 192 2
2268.4.ba \(\chi_{2268}(1079, \cdot)\) n/a 864 2
2268.4.bb \(\chi_{2268}(431, \cdot)\) n/a 1144 2
2268.4.be \(\chi_{2268}(1619, \cdot)\) n/a 1136 2
2268.4.bf \(\chi_{2268}(1459, \cdot)\) n/a 1136 2
2268.4.bi \(\chi_{2268}(55, \cdot)\) n/a 1144 2
2268.4.bj \(\chi_{2268}(271, \cdot)\) n/a 1144 2
2268.4.bm \(\chi_{2268}(593, \cdot)\) n/a 192 2
2268.4.bo \(\chi_{2268}(253, \cdot)\) n/a 324 6
2268.4.bp \(\chi_{2268}(289, \cdot)\) n/a 432 6
2268.4.bq \(\chi_{2268}(37, \cdot)\) n/a 432 6
2268.4.bs \(\chi_{2268}(611, \cdot)\) n/a 2568 6
2268.4.bt \(\chi_{2268}(451, \cdot)\) n/a 2568 6
2268.4.bx \(\chi_{2268}(125, \cdot)\) n/a 432 6
2268.4.ca \(\chi_{2268}(17, \cdot)\) n/a 432 6
2268.4.cc \(\chi_{2268}(307, \cdot)\) n/a 2568 6
2268.4.cd \(\chi_{2268}(19, \cdot)\) n/a 2568 6
2268.4.cf \(\chi_{2268}(71, \cdot)\) n/a 1944 6
2268.4.ci \(\chi_{2268}(179, \cdot)\) n/a 2568 6
2268.4.ck \(\chi_{2268}(341, \cdot)\) n/a 432 6
2268.4.cm \(\chi_{2268}(193, \cdot)\) n/a 3888 18
2268.4.cn \(\chi_{2268}(85, \cdot)\) n/a 2916 18
2268.4.co \(\chi_{2268}(25, \cdot)\) n/a 3888 18
2268.4.cr \(\chi_{2268}(5, \cdot)\) n/a 3888 18
2268.4.cs \(\chi_{2268}(11, \cdot)\) n/a 23256 18
2268.4.ct \(\chi_{2268}(139, \cdot)\) n/a 23256 18
2268.4.cu \(\chi_{2268}(31, \cdot)\) n/a 23256 18
2268.4.dd \(\chi_{2268}(155, \cdot)\) n/a 17496 18
2268.4.de \(\chi_{2268}(95, \cdot)\) n/a 23256 18
2268.4.df \(\chi_{2268}(173, \cdot)\) n/a 3888 18
2268.4.dg \(\chi_{2268}(41, \cdot)\) n/a 3888 18
2268.4.dh \(\chi_{2268}(103, \cdot)\) n/a 23256 18

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2268))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2268)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1134))\)\(^{\oplus 2}\)