Properties

Label 2288.2
Level 2288
Weight 2
Dimension 87254
Nonzero newspaces 56
Sturm bound 645120
Trace bound 25

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2288 = 2^{4} \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(645120\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2288))\).

Total New Old
Modular forms 164640 89038 75602
Cusp forms 157921 87254 70667
Eisenstein series 6719 1784 4935

Trace form

\( 87254 q - 160 q^{2} - 122 q^{3} - 152 q^{4} - 198 q^{5} - 136 q^{6} - 114 q^{7} - 136 q^{8} - 38 q^{9} + O(q^{10}) \) \( 87254 q - 160 q^{2} - 122 q^{3} - 152 q^{4} - 198 q^{5} - 136 q^{6} - 114 q^{7} - 136 q^{8} - 38 q^{9} - 152 q^{10} - 128 q^{11} - 368 q^{12} - 219 q^{13} - 360 q^{14} - 98 q^{15} - 184 q^{16} - 358 q^{17} - 144 q^{18} - 90 q^{19} - 136 q^{20} - 164 q^{21} - 176 q^{22} - 264 q^{23} - 152 q^{24} - 26 q^{25} - 164 q^{26} - 290 q^{27} - 120 q^{28} - 166 q^{29} - 168 q^{30} - 178 q^{31} - 120 q^{32} - 364 q^{33} - 336 q^{34} - 70 q^{35} - 168 q^{36} - 126 q^{37} - 200 q^{38} - 45 q^{39} - 376 q^{40} + 90 q^{41} - 152 q^{42} + 72 q^{43} - 184 q^{44} - 192 q^{45} - 104 q^{46} + 82 q^{47} - 120 q^{48} - 142 q^{49} - 176 q^{50} + 154 q^{51} - 180 q^{52} - 334 q^{53} - 152 q^{54} - 384 q^{56} + 98 q^{57} - 200 q^{58} - 66 q^{59} - 152 q^{60} - 142 q^{61} - 88 q^{62} - 32 q^{63} - 152 q^{64} - 326 q^{65} - 384 q^{66} - 280 q^{67} - 152 q^{68} - 208 q^{69} - 400 q^{70} - 134 q^{71} - 336 q^{72} - 198 q^{73} - 352 q^{74} - 206 q^{75} - 424 q^{76} - 366 q^{77} - 640 q^{78} - 358 q^{79} - 560 q^{80} - 506 q^{81} - 552 q^{82} - 222 q^{83} - 1000 q^{84} - 542 q^{85} - 664 q^{86} - 356 q^{87} - 920 q^{88} - 440 q^{89} - 1432 q^{90} - 277 q^{91} - 1048 q^{92} - 830 q^{93} - 1080 q^{94} - 382 q^{95} - 1480 q^{96} - 790 q^{97} - 1048 q^{98} - 332 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2288))\)

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
2288.2.a \(\chi_{2288}(1, \cdot)\) 2288.2.a.a 1 1
2288.2.a.b 1
2288.2.a.c 1
2288.2.a.d 1
2288.2.a.e 1
2288.2.a.f 1
2288.2.a.g 1
2288.2.a.h 1
2288.2.a.i 1
2288.2.a.j 1
2288.2.a.k 1
2288.2.a.l 1
2288.2.a.m 2
2288.2.a.n 2
2288.2.a.o 2
2288.2.a.p 2
2288.2.a.q 2
2288.2.a.r 2
2288.2.a.s 3
2288.2.a.t 3
2288.2.a.u 3
2288.2.a.v 3
2288.2.a.w 3
2288.2.a.x 4
2288.2.a.y 5
2288.2.a.z 6
2288.2.a.ba 6
2288.2.b \(\chi_{2288}(2287, \cdot)\) 2288.2.b.a 4 1
2288.2.b.b 24
2288.2.b.c 56
2288.2.d \(\chi_{2288}(1145, \cdot)\) None 0 1
2288.2.g \(\chi_{2288}(441, \cdot)\) None 0 1
2288.2.i \(\chi_{2288}(703, \cdot)\) 2288.2.i.a 24 1
2288.2.i.b 48
2288.2.j \(\chi_{2288}(1585, \cdot)\) 2288.2.j.a 2 1
2288.2.j.b 2
2288.2.j.c 2
2288.2.j.d 2
2288.2.j.e 2
2288.2.j.f 4
2288.2.j.g 4
2288.2.j.h 6
2288.2.j.i 8
2288.2.j.j 10
2288.2.j.k 12
2288.2.j.l 16
2288.2.l \(\chi_{2288}(1847, \cdot)\) None 0 1
2288.2.o \(\chi_{2288}(1143, \cdot)\) None 0 1
2288.2.q \(\chi_{2288}(529, \cdot)\) n/a 140 2
2288.2.s \(\chi_{2288}(463, \cdot)\) n/a 140 2
2288.2.t \(\chi_{2288}(681, \cdot)\) None 0 2
2288.2.v \(\chi_{2288}(1035, \cdot)\) n/a 560 2
2288.2.x \(\chi_{2288}(21, \cdot)\) n/a 664 2
2288.2.ba \(\chi_{2288}(131, \cdot)\) n/a 576 2
2288.2.bb \(\chi_{2288}(573, \cdot)\) n/a 480 2
2288.2.bd \(\chi_{2288}(1013, \cdot)\) n/a 560 2
2288.2.bg \(\chi_{2288}(571, \cdot)\) n/a 664 2
2288.2.bi \(\chi_{2288}(2179, \cdot)\) n/a 560 2
2288.2.bk \(\chi_{2288}(1165, \cdot)\) n/a 664 2
2288.2.bm \(\chi_{2288}(551, \cdot)\) None 0 2
2288.2.bn \(\chi_{2288}(593, \cdot)\) n/a 164 2
2288.2.bp \(\chi_{2288}(625, \cdot)\) n/a 288 4
2288.2.br \(\chi_{2288}(87, \cdot)\) None 0 2
2288.2.bt \(\chi_{2288}(881, \cdot)\) n/a 140 2
2288.2.bv \(\chi_{2288}(439, \cdot)\) None 0 2
2288.2.by \(\chi_{2288}(1673, \cdot)\) None 0 2
2288.2.ca \(\chi_{2288}(1583, \cdot)\) n/a 168 2
2288.2.cb \(\chi_{2288}(1231, \cdot)\) n/a 168 2
2288.2.cd \(\chi_{2288}(2025, \cdot)\) None 0 2
2288.2.cg \(\chi_{2288}(519, \cdot)\) None 0 4
2288.2.cj \(\chi_{2288}(183, \cdot)\) None 0 4
2288.2.cl \(\chi_{2288}(753, \cdot)\) n/a 328 4
2288.2.cm \(\chi_{2288}(79, \cdot)\) n/a 288 4
2288.2.co \(\chi_{2288}(25, \cdot)\) None 0 4
2288.2.cr \(\chi_{2288}(313, \cdot)\) None 0 4
2288.2.ct \(\chi_{2288}(415, \cdot)\) n/a 336 4
2288.2.cv \(\chi_{2288}(241, \cdot)\) n/a 328 4
2288.2.cw \(\chi_{2288}(375, \cdot)\) None 0 4
2288.2.cz \(\chi_{2288}(461, \cdot)\) n/a 1328 4
2288.2.db \(\chi_{2288}(67, \cdot)\) n/a 1120 4
2288.2.dc \(\chi_{2288}(43, \cdot)\) n/a 1328 4
2288.2.df \(\chi_{2288}(309, \cdot)\) n/a 1120 4
2288.2.dh \(\chi_{2288}(133, \cdot)\) n/a 1120 4
2288.2.di \(\chi_{2288}(659, \cdot)\) n/a 1328 4
2288.2.dk \(\chi_{2288}(197, \cdot)\) n/a 1328 4
2288.2.dm \(\chi_{2288}(331, \cdot)\) n/a 1120 4
2288.2.dp \(\chi_{2288}(505, \cdot)\) None 0 4
2288.2.dq \(\chi_{2288}(111, \cdot)\) n/a 280 4
2288.2.ds \(\chi_{2288}(81, \cdot)\) n/a 656 8
2288.2.dt \(\chi_{2288}(161, \cdot)\) n/a 656 8
2288.2.dw \(\chi_{2288}(135, \cdot)\) None 0 8
2288.2.dx \(\chi_{2288}(541, \cdot)\) n/a 2656 8
2288.2.dz \(\chi_{2288}(515, \cdot)\) n/a 2656 8
2288.2.ec \(\chi_{2288}(51, \cdot)\) n/a 2656 8
2288.2.ed \(\chi_{2288}(181, \cdot)\) n/a 2656 8
2288.2.ef \(\chi_{2288}(53, \cdot)\) n/a 2304 8
2288.2.ei \(\chi_{2288}(547, \cdot)\) n/a 2304 8
2288.2.ek \(\chi_{2288}(437, \cdot)\) n/a 2656 8
2288.2.em \(\chi_{2288}(203, \cdot)\) n/a 2656 8
2288.2.en \(\chi_{2288}(57, \cdot)\) None 0 8
2288.2.eq \(\chi_{2288}(31, \cdot)\) n/a 672 8
2288.2.es \(\chi_{2288}(361, \cdot)\) None 0 8
2288.2.eu \(\chi_{2288}(607, \cdot)\) n/a 672 8
2288.2.ev \(\chi_{2288}(95, \cdot)\) n/a 672 8
2288.2.ex \(\chi_{2288}(9, \cdot)\) None 0 8
2288.2.fa \(\chi_{2288}(855, \cdot)\) None 0 8
2288.2.fc \(\chi_{2288}(49, \cdot)\) n/a 656 8
2288.2.fe \(\chi_{2288}(503, \cdot)\) None 0 8
2288.2.fg \(\chi_{2288}(15, \cdot)\) n/a 1344 16
2288.2.fj \(\chi_{2288}(41, \cdot)\) None 0 16
2288.2.fl \(\chi_{2288}(115, \cdot)\) n/a 5312 16
2288.2.fn \(\chi_{2288}(149, \cdot)\) n/a 5312 16
2288.2.fo \(\chi_{2288}(35, \cdot)\) n/a 5312 16
2288.2.fr \(\chi_{2288}(269, \cdot)\) n/a 5312 16
2288.2.ft \(\chi_{2288}(69, \cdot)\) n/a 5312 16
2288.2.fu \(\chi_{2288}(283, \cdot)\) n/a 5312 16
2288.2.fw \(\chi_{2288}(59, \cdot)\) n/a 5312 16
2288.2.fy \(\chi_{2288}(85, \cdot)\) n/a 5312 16
2288.2.ga \(\chi_{2288}(71, \cdot)\) None 0 16
2288.2.gd \(\chi_{2288}(145, \cdot)\) n/a 1312 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2288))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2288)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1144))\)\(^{\oplus 2}\)