# Properties

 Label 2240.4 Level 2240 Weight 4 Dimension 217932 Nonzero newspaces 56 Sturm bound 1179648 Trace bound 81

## Defining parameters

 Level: $$N$$ = $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$56$$ Sturm bound: $$1179648$$ Trace bound: $$81$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2240))$$.

Total New Old
Modular forms 445824 219252 226572
Cusp forms 438912 217932 220980
Eisenstein series 6912 1320 5592

## Trace form

 $$217932 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 64 q^{7} - 160 q^{8} - 188 q^{9} + O(q^{10})$$ $$217932 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 64 q^{7} - 160 q^{8} - 188 q^{9} - 96 q^{10} - 224 q^{11} - 64 q^{12} + 224 q^{13} - 80 q^{14} + 64 q^{15} - 192 q^{16} + 304 q^{17} - 64 q^{18} + 48 q^{19} - 96 q^{20} - 264 q^{21} + 1728 q^{22} - 56 q^{23} + 3936 q^{24} + 232 q^{25} - 352 q^{26} - 792 q^{27} - 1600 q^{28} - 1760 q^{29} - 4736 q^{30} - 1592 q^{31} - 5024 q^{32} - 3976 q^{33} - 4064 q^{34} - 568 q^{35} - 4000 q^{36} - 2144 q^{37} + 1696 q^{38} - 40 q^{39} + 3184 q^{40} + 3856 q^{41} + 6240 q^{42} + 3224 q^{43} + 3936 q^{44} + 2872 q^{45} - 192 q^{46} + 3720 q^{47} - 64 q^{48} + 1300 q^{49} - 5952 q^{50} + 17752 q^{51} - 13312 q^{52} + 1568 q^{53} - 6976 q^{54} + 1088 q^{55} + 544 q^{56} - 4080 q^{57} + 9440 q^{58} - 17888 q^{59} + 9696 q^{60} - 4512 q^{61} + 11904 q^{62} - 12672 q^{63} + 24032 q^{64} + 3572 q^{65} + 21952 q^{66} - 16752 q^{67} + 8192 q^{68} + 3344 q^{69} + 1896 q^{70} - 3056 q^{71} - 2656 q^{72} - 720 q^{73} - 10592 q^{74} + 948 q^{75} - 24000 q^{76} - 840 q^{77} - 8128 q^{78} + 27608 q^{79} + 8432 q^{80} + 7876 q^{81} + 27776 q^{82} - 528 q^{83} + 8208 q^{84} - 6336 q^{85} - 2272 q^{86} - 5208 q^{87} - 12544 q^{88} - 12944 q^{89} - 18816 q^{90} + 4776 q^{91} - 50624 q^{92} + 8384 q^{93} - 35776 q^{94} + 13188 q^{95} - 51872 q^{96} - 3920 q^{97} - 24288 q^{98} + 3368 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2240))$$

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
2240.4.a $$\chi_{2240}(1, \cdot)$$ 2240.4.a.a 1 1
2240.4.a.b 1
2240.4.a.c 1
2240.4.a.d 1
2240.4.a.e 1
2240.4.a.f 1
2240.4.a.g 1
2240.4.a.h 1
2240.4.a.i 1
2240.4.a.j 1
2240.4.a.k 1
2240.4.a.l 1
2240.4.a.m 1
2240.4.a.n 1
2240.4.a.o 1
2240.4.a.p 1
2240.4.a.q 1
2240.4.a.r 1
2240.4.a.s 1
2240.4.a.t 1
2240.4.a.u 1
2240.4.a.v 1
2240.4.a.w 1
2240.4.a.x 1
2240.4.a.y 1
2240.4.a.z 1
2240.4.a.ba 1
2240.4.a.bb 1
2240.4.a.bc 1
2240.4.a.bd 1
2240.4.a.be 1
2240.4.a.bf 1
2240.4.a.bg 1
2240.4.a.bh 1
2240.4.a.bi 1
2240.4.a.bj 1
2240.4.a.bk 1
2240.4.a.bl 1
2240.4.a.bm 2
2240.4.a.bn 2
2240.4.a.bo 2
2240.4.a.bp 2
2240.4.a.bq 3
2240.4.a.br 3
2240.4.a.bs 3
2240.4.a.bt 3
2240.4.a.bu 3
2240.4.a.bv 3
2240.4.a.bw 3
2240.4.a.bx 3
2240.4.a.by 3
2240.4.a.bz 3
2240.4.a.ca 4
2240.4.a.cb 4
2240.4.a.cc 4
2240.4.a.cd 4
2240.4.a.ce 4
2240.4.a.cf 4
2240.4.a.cg 4
2240.4.a.ch 4
2240.4.a.ci 4
2240.4.a.cj 4
2240.4.a.ck 4
2240.4.a.cl 4
2240.4.a.cm 5
2240.4.a.cn 5
2240.4.a.co 5
2240.4.a.cp 5
2240.4.b $$\chi_{2240}(1121, \cdot)$$ n/a 144 1
2240.4.e $$\chi_{2240}(2239, \cdot)$$ n/a 284 1
2240.4.g $$\chi_{2240}(449, \cdot)$$ n/a 216 1
2240.4.h $$\chi_{2240}(671, \cdot)$$ n/a 192 1
2240.4.k $$\chi_{2240}(1791, \cdot)$$ n/a 192 1
2240.4.l $$\chi_{2240}(1569, \cdot)$$ n/a 216 1
2240.4.n $$\chi_{2240}(1119, \cdot)$$ n/a 288 1
2240.4.q $$\chi_{2240}(641, \cdot)$$ n/a 384 2
2240.4.r $$\chi_{2240}(433, \cdot)$$ n/a 568 2
2240.4.t $$\chi_{2240}(463, \cdot)$$ n/a 432 2
2240.4.w $$\chi_{2240}(97, \cdot)$$ n/a 576 2
2240.4.x $$\chi_{2240}(127, \cdot)$$ n/a 432 2
2240.4.bb $$\chi_{2240}(1009, \cdot)$$ n/a 432 2
2240.4.bc $$\chi_{2240}(111, \cdot)$$ n/a 384 2
2240.4.bd $$\chi_{2240}(561, \cdot)$$ n/a 288 2
2240.4.be $$\chi_{2240}(559, \cdot)$$ n/a 568 2
2240.4.bi $$\chi_{2240}(1247, \cdot)$$ n/a 432 2
2240.4.bj $$\chi_{2240}(1217, \cdot)$$ n/a 568 2
2240.4.bl $$\chi_{2240}(1583, \cdot)$$ n/a 432 2
2240.4.bn $$\chi_{2240}(1553, \cdot)$$ n/a 568 2
2240.4.bq $$\chi_{2240}(159, \cdot)$$ n/a 576 2
2240.4.bs $$\chi_{2240}(831, \cdot)$$ n/a 384 2
2240.4.bv $$\chi_{2240}(289, \cdot)$$ n/a 576 2
2240.4.bw $$\chi_{2240}(1089, \cdot)$$ n/a 568 2
2240.4.bz $$\chi_{2240}(31, \cdot)$$ n/a 384 2
2240.4.cb $$\chi_{2240}(1761, \cdot)$$ n/a 384 2
2240.4.cc $$\chi_{2240}(1279, \cdot)$$ n/a 568 2
2240.4.cg $$\chi_{2240}(281, \cdot)$$ None 0 4
2240.4.ch $$\chi_{2240}(279, \cdot)$$ None 0 4
2240.4.ci $$\chi_{2240}(377, \cdot)$$ None 0 4
2240.4.cj $$\chi_{2240}(407, \cdot)$$ None 0 4
2240.4.cm $$\chi_{2240}(183, \cdot)$$ None 0 4
2240.4.cn $$\chi_{2240}(153, \cdot)$$ None 0 4
2240.4.cs $$\chi_{2240}(391, \cdot)$$ None 0 4
2240.4.ct $$\chi_{2240}(169, \cdot)$$ None 0 4
2240.4.cv $$\chi_{2240}(207, \cdot)$$ n/a 1136 4
2240.4.cx $$\chi_{2240}(593, \cdot)$$ n/a 1136 4
2240.4.cy $$\chi_{2240}(257, \cdot)$$ n/a 1136 4
2240.4.db $$\chi_{2240}(543, \cdot)$$ n/a 1152 4
2240.4.de $$\chi_{2240}(719, \cdot)$$ n/a 1136 4
2240.4.df $$\chi_{2240}(81, \cdot)$$ n/a 768 4
2240.4.dg $$\chi_{2240}(271, \cdot)$$ n/a 768 4
2240.4.dh $$\chi_{2240}(529, \cdot)$$ n/a 1136 4
2240.4.dk $$\chi_{2240}(767, \cdot)$$ n/a 1136 4
2240.4.dn $$\chi_{2240}(33, \cdot)$$ n/a 1152 4
2240.4.dp $$\chi_{2240}(17, \cdot)$$ n/a 1136 4
2240.4.dr $$\chi_{2240}(1103, \cdot)$$ n/a 1136 4
2240.4.du $$\chi_{2240}(13, \cdot)$$ n/a 9184 8
2240.4.dv $$\chi_{2240}(43, \cdot)$$ n/a 6912 8
2240.4.dw $$\chi_{2240}(139, \cdot)$$ n/a 9184 8
2240.4.dx $$\chi_{2240}(141, \cdot)$$ n/a 4608 8
2240.4.dy $$\chi_{2240}(251, \cdot)$$ n/a 6144 8
2240.4.dz $$\chi_{2240}(29, \cdot)$$ n/a 6912 8
2240.4.eg $$\chi_{2240}(267, \cdot)$$ n/a 6912 8
2240.4.eh $$\chi_{2240}(237, \cdot)$$ n/a 9184 8
2240.4.ei $$\chi_{2240}(9, \cdot)$$ None 0 8
2240.4.ej $$\chi_{2240}(311, \cdot)$$ None 0 8
2240.4.eo $$\chi_{2240}(23, \cdot)$$ None 0 8
2240.4.ep $$\chi_{2240}(297, \cdot)$$ None 0 8
2240.4.es $$\chi_{2240}(73, \cdot)$$ None 0 8
2240.4.et $$\chi_{2240}(247, \cdot)$$ None 0 8
2240.4.eu $$\chi_{2240}(199, \cdot)$$ None 0 8
2240.4.ev $$\chi_{2240}(121, \cdot)$$ None 0 8
2240.4.ey $$\chi_{2240}(157, \cdot)$$ n/a 18368 16
2240.4.ez $$\chi_{2240}(107, \cdot)$$ n/a 18368 16
2240.4.fg $$\chi_{2240}(109, \cdot)$$ n/a 18368 16
2240.4.fh $$\chi_{2240}(131, \cdot)$$ n/a 12288 16
2240.4.fi $$\chi_{2240}(221, \cdot)$$ n/a 12288 16
2240.4.fj $$\chi_{2240}(19, \cdot)$$ n/a 18368 16
2240.4.fk $$\chi_{2240}(67, \cdot)$$ n/a 18368 16
2240.4.fl $$\chi_{2240}(117, \cdot)$$ n/a 18368 16

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2240))$$ into lower level spaces

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