Properties

Label 2880.2
Level 2880
Weight 2
Dimension 89694
Nonzero newspaces 56
Sturm bound 884736
Trace bound 81

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Defining parameters

Level: \( N \) = \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(884736\)
Trace bound: \(81\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2880))\).

Total New Old
Modular forms 225792 90882 134910
Cusp forms 216577 89694 126883
Eisenstein series 9215 1188 8027

Trace form

\( 89694q - 48q^{2} - 48q^{3} - 48q^{4} - 72q^{5} - 192q^{6} - 32q^{7} - 48q^{8} - 80q^{9} + O(q^{10}) \) \( 89694q - 48q^{2} - 48q^{3} - 48q^{4} - 72q^{5} - 192q^{6} - 32q^{7} - 48q^{8} - 80q^{9} - 216q^{10} - 100q^{11} - 64q^{12} - 32q^{13} - 48q^{14} - 72q^{15} - 144q^{16} - 68q^{17} - 64q^{18} - 92q^{19} - 72q^{20} - 192q^{21} - 64q^{22} - 48q^{23} - 64q^{24} - 106q^{25} - 224q^{26} - 48q^{27} - 224q^{28} - 80q^{29} - 96q^{30} - 152q^{31} - 128q^{32} - 72q^{33} - 128q^{34} - 96q^{35} - 192q^{36} - 224q^{37} - 128q^{38} - 96q^{39} - 112q^{40} - 308q^{41} - 64q^{42} - 140q^{43} - 64q^{44} - 144q^{45} - 432q^{46} - 144q^{47} - 64q^{48} - 194q^{49} - 48q^{50} - 224q^{51} + 48q^{52} - 192q^{53} - 64q^{54} - 288q^{55} - 32q^{56} - 144q^{57} + 96q^{58} - 268q^{59} - 96q^{60} - 192q^{61} + 144q^{62} - 104q^{63} + 48q^{64} - 268q^{65} - 192q^{66} - 260q^{67} + 48q^{68} - 16q^{69} + 24q^{70} - 288q^{71} - 64q^{72} - 244q^{73} + 64q^{74} - 84q^{75} - 16q^{76} + 72q^{77} + 32q^{78} - 104q^{79} + 144q^{80} - 208q^{81} + 336q^{82} + 44q^{83} + 384q^{84} - 48q^{85} + 480q^{86} + 64q^{87} + 432q^{88} + 292q^{89} + 192q^{90} - 184q^{91} + 864q^{92} + 128q^{93} + 528q^{94} + 48q^{95} + 352q^{96} + 364q^{97} + 768q^{98} + 80q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2880))\)

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
2880.2.a \(\chi_{2880}(1, \cdot)\) 2880.2.a.a 1 1
2880.2.a.b 1
2880.2.a.c 1
2880.2.a.d 1
2880.2.a.e 1
2880.2.a.f 1
2880.2.a.g 1
2880.2.a.h 1
2880.2.a.i 1
2880.2.a.j 1
2880.2.a.k 1
2880.2.a.l 1
2880.2.a.m 1
2880.2.a.n 1
2880.2.a.o 1
2880.2.a.p 1
2880.2.a.q 1
2880.2.a.r 1
2880.2.a.s 1
2880.2.a.t 1
2880.2.a.u 1
2880.2.a.v 1
2880.2.a.w 1
2880.2.a.x 1
2880.2.a.y 1
2880.2.a.z 1
2880.2.a.ba 1
2880.2.a.bb 1
2880.2.a.bc 1
2880.2.a.bd 1
2880.2.a.be 1
2880.2.a.bf 1
2880.2.a.bg 1
2880.2.a.bh 1
2880.2.a.bi 2
2880.2.a.bj 2
2880.2.a.bk 2
2880.2.b \(\chi_{2880}(2591, \cdot)\) 2880.2.b.a 8 1
2880.2.b.b 8
2880.2.b.c 8
2880.2.b.d 8
2880.2.d \(\chi_{2880}(289, \cdot)\) 2880.2.d.a 2 1
2880.2.d.b 2
2880.2.d.c 2
2880.2.d.d 2
2880.2.d.e 4
2880.2.d.f 8
2880.2.d.g 8
2880.2.d.h 8
2880.2.d.i 8
2880.2.d.j 8
2880.2.d.k 8
2880.2.f \(\chi_{2880}(1729, \cdot)\) 2880.2.f.a 2 1
2880.2.f.b 2
2880.2.f.c 2
2880.2.f.d 2
2880.2.f.e 2
2880.2.f.f 2
2880.2.f.g 2
2880.2.f.h 2
2880.2.f.i 2
2880.2.f.j 2
2880.2.f.k 2
2880.2.f.l 2
2880.2.f.m 2
2880.2.f.n 2
2880.2.f.o 2
2880.2.f.p 2
2880.2.f.q 2
2880.2.f.r 2
2880.2.f.s 2
2880.2.f.t 2
2880.2.f.u 2
2880.2.f.v 4
2880.2.f.w 4
2880.2.f.x 8
2880.2.h \(\chi_{2880}(1151, \cdot)\) 2880.2.h.a 4 1
2880.2.h.b 4
2880.2.h.c 4
2880.2.h.d 4
2880.2.h.e 8
2880.2.h.f 8
2880.2.k \(\chi_{2880}(1441, \cdot)\) 2880.2.k.a 2 1
2880.2.k.b 2
2880.2.k.c 2
2880.2.k.d 2
2880.2.k.e 4
2880.2.k.f 4
2880.2.k.g 4
2880.2.k.h 4
2880.2.k.i 4
2880.2.k.j 4
2880.2.k.k 4
2880.2.k.l 4
2880.2.m \(\chi_{2880}(1439, \cdot)\) 2880.2.m.a 8 1
2880.2.m.b 8
2880.2.m.c 32
2880.2.o \(\chi_{2880}(2879, \cdot)\) 2880.2.o.a 4 1
2880.2.o.b 4
2880.2.o.c 8
2880.2.o.d 8
2880.2.o.e 12
2880.2.o.f 12
2880.2.q \(\chi_{2880}(961, \cdot)\) n/a 192 2
2880.2.t \(\chi_{2880}(721, \cdot)\) 2880.2.t.a 4 2
2880.2.t.b 8
2880.2.t.c 16
2880.2.t.d 20
2880.2.t.e 32
2880.2.u \(\chi_{2880}(719, \cdot)\) 2880.2.u.a 96 2
2880.2.w \(\chi_{2880}(2177, \cdot)\) 2880.2.w.a 4 2
2880.2.w.b 4
2880.2.w.c 4
2880.2.w.d 4
2880.2.w.e 4
2880.2.w.f 4
2880.2.w.g 4
2880.2.w.h 4
2880.2.w.i 4
2880.2.w.j 4
2880.2.w.k 4
2880.2.w.l 4
2880.2.w.m 8
2880.2.w.n 8
2880.2.w.o 8
2880.2.w.p 12
2880.2.w.q 12
2880.2.x \(\chi_{2880}(127, \cdot)\) n/a 116 2
2880.2.z \(\chi_{2880}(847, \cdot)\) n/a 116 2
2880.2.bc \(\chi_{2880}(593, \cdot)\) 2880.2.bc.a 96 2
2880.2.bd \(\chi_{2880}(1423, \cdot)\) n/a 116 2
2880.2.bg \(\chi_{2880}(17, \cdot)\) 2880.2.bg.a 96 2
2880.2.bi \(\chi_{2880}(1567, \cdot)\) n/a 120 2
2880.2.bj \(\chi_{2880}(737, \cdot)\) 2880.2.bj.a 8 2
2880.2.bj.b 8
2880.2.bj.c 8
2880.2.bj.d 8
2880.2.bj.e 32
2880.2.bj.f 32
2880.2.bl \(\chi_{2880}(431, \cdot)\) 2880.2.bl.a 8 2
2880.2.bl.b 24
2880.2.bl.c 32
2880.2.bm \(\chi_{2880}(1009, \cdot)\) n/a 116 2
2880.2.br \(\chi_{2880}(959, \cdot)\) n/a 280 2
2880.2.bt \(\chi_{2880}(479, \cdot)\) n/a 288 2
2880.2.bv \(\chi_{2880}(481, \cdot)\) n/a 192 2
2880.2.bw \(\chi_{2880}(191, \cdot)\) n/a 192 2
2880.2.by \(\chi_{2880}(769, \cdot)\) n/a 280 2
2880.2.ca \(\chi_{2880}(1249, \cdot)\) n/a 288 2
2880.2.cc \(\chi_{2880}(671, \cdot)\) n/a 192 2
2880.2.ce \(\chi_{2880}(1063, \cdot)\) None 0 4
2880.2.ch \(\chi_{2880}(233, \cdot)\) None 0 4
2880.2.ci \(\chi_{2880}(359, \cdot)\) None 0 4
2880.2.cl \(\chi_{2880}(361, \cdot)\) None 0 4
2880.2.cn \(\chi_{2880}(71, \cdot)\) None 0 4
2880.2.co \(\chi_{2880}(649, \cdot)\) None 0 4
2880.2.cr \(\chi_{2880}(953, \cdot)\) None 0 4
2880.2.cs \(\chi_{2880}(343, \cdot)\) None 0 4
2880.2.cu \(\chi_{2880}(49, \cdot)\) n/a 560 4
2880.2.cv \(\chi_{2880}(911, \cdot)\) n/a 384 4
2880.2.cy \(\chi_{2880}(223, \cdot)\) n/a 576 4
2880.2.db \(\chi_{2880}(353, \cdot)\) n/a 576 4
2880.2.dc \(\chi_{2880}(113, \cdot)\) n/a 560 4
2880.2.df \(\chi_{2880}(367, \cdot)\) n/a 560 4
2880.2.dg \(\chi_{2880}(497, \cdot)\) n/a 560 4
2880.2.dj \(\chi_{2880}(943, \cdot)\) n/a 560 4
2880.2.dk \(\chi_{2880}(257, \cdot)\) n/a 560 4
2880.2.dn \(\chi_{2880}(1087, \cdot)\) n/a 560 4
2880.2.dq \(\chi_{2880}(239, \cdot)\) n/a 560 4
2880.2.dr \(\chi_{2880}(241, \cdot)\) n/a 384 4
2880.2.dt \(\chi_{2880}(197, \cdot)\) n/a 1536 8
2880.2.du \(\chi_{2880}(307, \cdot)\) n/a 1904 8
2880.2.dw \(\chi_{2880}(181, \cdot)\) n/a 1280 8
2880.2.dy \(\chi_{2880}(109, \cdot)\) n/a 1904 8
2880.2.eb \(\chi_{2880}(251, \cdot)\) n/a 1024 8
2880.2.ed \(\chi_{2880}(179, \cdot)\) n/a 1536 8
2880.2.ef \(\chi_{2880}(53, \cdot)\) n/a 1536 8
2880.2.eg \(\chi_{2880}(163, \cdot)\) n/a 1904 8
2880.2.ej \(\chi_{2880}(7, \cdot)\) None 0 8
2880.2.ek \(\chi_{2880}(137, \cdot)\) None 0 8
2880.2.em \(\chi_{2880}(121, \cdot)\) None 0 8
2880.2.ep \(\chi_{2880}(119, \cdot)\) None 0 8
2880.2.er \(\chi_{2880}(169, \cdot)\) None 0 8
2880.2.es \(\chi_{2880}(311, \cdot)\) None 0 8
2880.2.eu \(\chi_{2880}(713, \cdot)\) None 0 8
2880.2.ex \(\chi_{2880}(103, \cdot)\) None 0 8
2880.2.ey \(\chi_{2880}(43, \cdot)\) n/a 9152 16
2880.2.fb \(\chi_{2880}(173, \cdot)\) n/a 9152 16
2880.2.fd \(\chi_{2880}(59, \cdot)\) n/a 9152 16
2880.2.ff \(\chi_{2880}(11, \cdot)\) n/a 6144 16
2880.2.fg \(\chi_{2880}(229, \cdot)\) n/a 9152 16
2880.2.fi \(\chi_{2880}(61, \cdot)\) n/a 6144 16
2880.2.fk \(\chi_{2880}(187, \cdot)\) n/a 9152 16
2880.2.fn \(\chi_{2880}(77, \cdot)\) n/a 9152 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1440))\)\(^{\oplus 2}\)