# Properties

 Label 2240.2 Level 2240 Weight 2 Dimension 72204 Nonzero newspaces 56 Sturm bound 589824 Trace bound 81

## Defining parameters

 Level: $$N$$ = $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$589824$$ Trace bound: $$81$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2240))$$.

Total New Old
Modular forms 150912 73524 77388
Cusp forms 144001 72204 71797
Eisenstein series 6911 1320 5591

## Trace form

 $$72204q - 64q^{2} - 48q^{3} - 64q^{4} - 96q^{5} - 192q^{6} - 64q^{7} - 160q^{8} - 92q^{9} + O(q^{10})$$ $$72204q - 64q^{2} - 48q^{3} - 64q^{4} - 96q^{5} - 192q^{6} - 64q^{7} - 160q^{8} - 92q^{9} - 96q^{10} - 160q^{11} - 64q^{12} - 96q^{13} - 80q^{14} - 192q^{15} - 192q^{16} - 144q^{17} - 64q^{18} - 80q^{19} - 96q^{20} - 232q^{21} - 128q^{22} - 56q^{23} + 96q^{24} - 88q^{25} - 32q^{26} - 24q^{27} - 96q^{29} + 64q^{30} - 56q^{31} + 96q^{32} + 56q^{33} + 96q^{34} - 88q^{35} - 160q^{36} - 32q^{37} + 96q^{38} - 40q^{39} - 16q^{40} - 240q^{41} - 168q^{43} - 32q^{44} - 104q^{45} - 192q^{46} - 120q^{47} - 64q^{48} - 172q^{49} - 288q^{50} - 40q^{51} - 256q^{52} - 160q^{53} - 320q^{54} + 64q^{55} - 352q^{56} - 176q^{57} - 352q^{58} + 224q^{59} - 288q^{60} - 224q^{61} - 192q^{62} + 128q^{63} - 544q^{64} - 204q^{65} - 512q^{66} + 400q^{67} - 256q^{68} + 80q^{69} - 216q^{70} + 16q^{71} - 352q^{72} + 48q^{73} - 288q^{74} + 244q^{75} - 448q^{76} + 24q^{77} - 256q^{78} + 216q^{79} - 16q^{80} + 4q^{81} + 256q^{82} + 112q^{83} + 144q^{84} - 32q^{85} + 224q^{86} + 168q^{87} + 256q^{88} + 240q^{89} + 192q^{90} + 40q^{91} + 448q^{92} + 384q^{93} + 320q^{94} + 132q^{95} + 352q^{96} + 368q^{97} + 192q^{98} + 360q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2240))$$

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
2240.2.a $$\chi_{2240}(1, \cdot)$$ 2240.2.a.a 1 1
2240.2.a.b 1
2240.2.a.c 1
2240.2.a.d 1
2240.2.a.e 1
2240.2.a.f 1
2240.2.a.g 1
2240.2.a.h 1
2240.2.a.i 1
2240.2.a.j 1
2240.2.a.k 1
2240.2.a.l 1
2240.2.a.m 1
2240.2.a.n 1
2240.2.a.o 1
2240.2.a.p 1
2240.2.a.q 1
2240.2.a.r 1
2240.2.a.s 1
2240.2.a.t 1
2240.2.a.u 1
2240.2.a.v 1
2240.2.a.w 1
2240.2.a.x 1
2240.2.a.y 1
2240.2.a.z 1
2240.2.a.ba 1
2240.2.a.bb 1
2240.2.a.bc 2
2240.2.a.bd 2
2240.2.a.be 2
2240.2.a.bf 2
2240.2.a.bg 2
2240.2.a.bh 2
2240.2.a.bi 2
2240.2.a.bj 2
2240.2.a.bk 2
2240.2.a.bl 2
2240.2.b $$\chi_{2240}(1121, \cdot)$$ 2240.2.b.a 2 1
2240.2.b.b 2
2240.2.b.c 4
2240.2.b.d 4
2240.2.b.e 6
2240.2.b.f 6
2240.2.b.g 12
2240.2.b.h 12
2240.2.e $$\chi_{2240}(2239, \cdot)$$ 2240.2.e.a 4 1
2240.2.e.b 4
2240.2.e.c 4
2240.2.e.d 8
2240.2.e.e 8
2240.2.e.f 16
2240.2.e.g 48
2240.2.g $$\chi_{2240}(449, \cdot)$$ 2240.2.g.a 2 1
2240.2.g.b 2
2240.2.g.c 2
2240.2.g.d 2
2240.2.g.e 2
2240.2.g.f 2
2240.2.g.g 2
2240.2.g.h 2
2240.2.g.i 4
2240.2.g.j 4
2240.2.g.k 4
2240.2.g.l 6
2240.2.g.m 6
2240.2.g.n 10
2240.2.g.o 10
2240.2.g.p 12
2240.2.h $$\chi_{2240}(671, \cdot)$$ 2240.2.h.a 4 1
2240.2.h.b 4
2240.2.h.c 4
2240.2.h.d 4
2240.2.h.e 24
2240.2.h.f 24
2240.2.k $$\chi_{2240}(1791, \cdot)$$ 2240.2.k.a 4 1
2240.2.k.b 4
2240.2.k.c 8
2240.2.k.d 8
2240.2.k.e 8
2240.2.k.f 16
2240.2.k.g 16
2240.2.l $$\chi_{2240}(1569, \cdot)$$ 2240.2.l.a 12 1
2240.2.l.b 12
2240.2.l.c 24
2240.2.l.d 24
2240.2.n $$\chi_{2240}(1119, \cdot)$$ 2240.2.n.a 8 1
2240.2.n.b 8
2240.2.n.c 8
2240.2.n.d 8
2240.2.n.e 8
2240.2.n.f 8
2240.2.n.g 8
2240.2.n.h 8
2240.2.n.i 16
2240.2.n.j 16
2240.2.q $$\chi_{2240}(641, \cdot)$$ n/a 128 2
2240.2.r $$\chi_{2240}(433, \cdot)$$ n/a 184 2
2240.2.t $$\chi_{2240}(463, \cdot)$$ n/a 144 2
2240.2.w $$\chi_{2240}(97, \cdot)$$ n/a 192 2
2240.2.x $$\chi_{2240}(127, \cdot)$$ n/a 144 2
2240.2.bb $$\chi_{2240}(1009, \cdot)$$ n/a 144 2
2240.2.bc $$\chi_{2240}(111, \cdot)$$ n/a 128 2
2240.2.bd $$\chi_{2240}(561, \cdot)$$ 2240.2.bd.a 44 2
2240.2.bd.b 52
2240.2.be $$\chi_{2240}(559, \cdot)$$ n/a 184 2
2240.2.bi $$\chi_{2240}(1247, \cdot)$$ n/a 144 2
2240.2.bj $$\chi_{2240}(1217, \cdot)$$ n/a 184 2
2240.2.bl $$\chi_{2240}(1583, \cdot)$$ n/a 144 2
2240.2.bn $$\chi_{2240}(1553, \cdot)$$ n/a 184 2
2240.2.bq $$\chi_{2240}(159, \cdot)$$ n/a 192 2
2240.2.bs $$\chi_{2240}(831, \cdot)$$ n/a 128 2
2240.2.bv $$\chi_{2240}(289, \cdot)$$ n/a 192 2
2240.2.bw $$\chi_{2240}(1089, \cdot)$$ n/a 184 2
2240.2.bz $$\chi_{2240}(31, \cdot)$$ n/a 128 2
2240.2.cb $$\chi_{2240}(1761, \cdot)$$ n/a 128 2
2240.2.cc $$\chi_{2240}(1279, \cdot)$$ n/a 184 2
2240.2.cg $$\chi_{2240}(281, \cdot)$$ None 0 4
2240.2.ch $$\chi_{2240}(279, \cdot)$$ None 0 4
2240.2.ci $$\chi_{2240}(377, \cdot)$$ None 0 4
2240.2.cj $$\chi_{2240}(407, \cdot)$$ None 0 4
2240.2.cm $$\chi_{2240}(183, \cdot)$$ None 0 4
2240.2.cn $$\chi_{2240}(153, \cdot)$$ None 0 4
2240.2.cs $$\chi_{2240}(391, \cdot)$$ None 0 4
2240.2.ct $$\chi_{2240}(169, \cdot)$$ None 0 4
2240.2.cv $$\chi_{2240}(207, \cdot)$$ n/a 368 4
2240.2.cx $$\chi_{2240}(593, \cdot)$$ n/a 368 4
2240.2.cy $$\chi_{2240}(257, \cdot)$$ n/a 368 4
2240.2.db $$\chi_{2240}(543, \cdot)$$ n/a 384 4
2240.2.de $$\chi_{2240}(719, \cdot)$$ n/a 368 4
2240.2.df $$\chi_{2240}(81, \cdot)$$ n/a 256 4
2240.2.dg $$\chi_{2240}(271, \cdot)$$ n/a 256 4
2240.2.dh $$\chi_{2240}(529, \cdot)$$ n/a 368 4
2240.2.dk $$\chi_{2240}(767, \cdot)$$ n/a 368 4
2240.2.dn $$\chi_{2240}(33, \cdot)$$ n/a 384 4
2240.2.dp $$\chi_{2240}(17, \cdot)$$ n/a 368 4
2240.2.dr $$\chi_{2240}(1103, \cdot)$$ n/a 368 4
2240.2.du $$\chi_{2240}(13, \cdot)$$ n/a 3040 8
2240.2.dv $$\chi_{2240}(43, \cdot)$$ n/a 2304 8
2240.2.dw $$\chi_{2240}(139, \cdot)$$ n/a 3040 8
2240.2.dx $$\chi_{2240}(141, \cdot)$$ n/a 1536 8
2240.2.dy $$\chi_{2240}(251, \cdot)$$ n/a 2048 8
2240.2.dz $$\chi_{2240}(29, \cdot)$$ n/a 2304 8
2240.2.eg $$\chi_{2240}(267, \cdot)$$ n/a 2304 8
2240.2.eh $$\chi_{2240}(237, \cdot)$$ n/a 3040 8
2240.2.ei $$\chi_{2240}(9, \cdot)$$ None 0 8
2240.2.ej $$\chi_{2240}(311, \cdot)$$ None 0 8
2240.2.eo $$\chi_{2240}(23, \cdot)$$ None 0 8
2240.2.ep $$\chi_{2240}(297, \cdot)$$ None 0 8
2240.2.es $$\chi_{2240}(73, \cdot)$$ None 0 8
2240.2.et $$\chi_{2240}(247, \cdot)$$ None 0 8
2240.2.eu $$\chi_{2240}(199, \cdot)$$ None 0 8
2240.2.ev $$\chi_{2240}(121, \cdot)$$ None 0 8
2240.2.ey $$\chi_{2240}(157, \cdot)$$ n/a 6080 16
2240.2.ez $$\chi_{2240}(107, \cdot)$$ n/a 6080 16
2240.2.fg $$\chi_{2240}(109, \cdot)$$ n/a 6080 16
2240.2.fh $$\chi_{2240}(131, \cdot)$$ n/a 4096 16
2240.2.fi $$\chi_{2240}(221, \cdot)$$ n/a 4096 16
2240.2.fj $$\chi_{2240}(19, \cdot)$$ n/a 6080 16
2240.2.fk $$\chi_{2240}(67, \cdot)$$ n/a 6080 16
2240.2.fl $$\chi_{2240}(117, \cdot)$$ n/a 6080 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2240))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2240)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(560))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1120))$$$$^{\oplus 2}$$