# Properties

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

## 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

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

## 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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(2880)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 42}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 21}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(480))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(576))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(720))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(960))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1440))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2880))$$$$^{\oplus 1}$$