# Properties

 Label 1440.2 Level 1440 Weight 2 Dimension 22302 Nonzero newspaces 40 Sturm bound 221184 Trace bound 53

## Defining parameters

 Level: $$N$$ = $$1440 = 2^{5} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$221184$$ Trace bound: $$53$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1440))$$.

Total New Old
Modular forms 57344 22842 34502
Cusp forms 53249 22302 30947
Eisenstein series 4095 540 3555

## Trace form

 $$22302 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 34 q^{5} - 96 q^{6} - 16 q^{7} - 24 q^{8} - 48 q^{9} + O(q^{10})$$ $$22302 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 34 q^{5} - 96 q^{6} - 16 q^{7} - 24 q^{8} - 48 q^{9} - 116 q^{10} - 60 q^{11} - 32 q^{12} - 36 q^{13} - 56 q^{14} - 42 q^{15} - 112 q^{16} - 52 q^{17} - 32 q^{18} - 88 q^{19} - 52 q^{20} - 128 q^{21} - 48 q^{22} - 72 q^{23} - 32 q^{24} - 82 q^{25} - 32 q^{26} - 48 q^{27} - 32 q^{28} - 76 q^{29} - 32 q^{30} - 140 q^{31} + 16 q^{32} - 72 q^{33} - 72 q^{35} - 48 q^{36} - 44 q^{37} + 184 q^{38} - 12 q^{39} + 80 q^{40} - 36 q^{41} + 128 q^{42} + 248 q^{44} - 24 q^{46} + 72 q^{47} + 176 q^{48} + 94 q^{49} + 132 q^{50} - 8 q^{51} + 216 q^{52} + 100 q^{53} + 144 q^{54} - 56 q^{55} + 224 q^{56} + 48 q^{57} + 240 q^{58} + 124 q^{59} + 8 q^{60} - 84 q^{61} + 48 q^{62} + 84 q^{63} + 48 q^{64} + 24 q^{65} - 96 q^{66} + 56 q^{67} + 176 q^{68} + 96 q^{69} + 120 q^{70} + 96 q^{71} - 32 q^{72} - 132 q^{73} + 120 q^{74} + 26 q^{75} + 56 q^{76} + 104 q^{77} - 80 q^{78} + 164 q^{79} + 112 q^{81} - 232 q^{82} + 376 q^{83} - 256 q^{84} + 28 q^{85} - 320 q^{86} + 316 q^{87} - 176 q^{88} + 148 q^{89} - 192 q^{90} + 200 q^{91} - 416 q^{92} - 32 q^{93} - 256 q^{94} + 296 q^{95} - 368 q^{96} + 60 q^{97} - 416 q^{98} + 332 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1440))$$

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
1440.2.a $$\chi_{1440}(1, \cdot)$$ 1440.2.a.a 1 1
1440.2.a.b 1
1440.2.a.c 1
1440.2.a.d 1
1440.2.a.e 1
1440.2.a.f 1
1440.2.a.g 1
1440.2.a.h 1
1440.2.a.i 1
1440.2.a.j 1
1440.2.a.k 1
1440.2.a.l 1
1440.2.a.m 1
1440.2.a.n 1
1440.2.a.o 2
1440.2.a.p 2
1440.2.a.q 2
1440.2.b $$\chi_{1440}(431, \cdot)$$ 1440.2.b.a 2 1
1440.2.b.b 2
1440.2.b.c 6
1440.2.b.d 6
1440.2.d $$\chi_{1440}(1009, \cdot)$$ 1440.2.d.a 4 1
1440.2.d.b 4
1440.2.d.c 4
1440.2.d.d 4
1440.2.d.e 6
1440.2.d.f 6
1440.2.f $$\chi_{1440}(289, \cdot)$$ 1440.2.f.a 2 1
1440.2.f.b 2
1440.2.f.c 2
1440.2.f.d 2
1440.2.f.e 2
1440.2.f.f 2
1440.2.f.g 2
1440.2.f.h 4
1440.2.f.i 4
1440.2.f.j 8
1440.2.h $$\chi_{1440}(1151, \cdot)$$ 1440.2.h.a 4 1
1440.2.h.b 4
1440.2.h.c 4
1440.2.h.d 4
1440.2.k $$\chi_{1440}(721, \cdot)$$ 1440.2.k.a 2 1
1440.2.k.b 2
1440.2.k.c 2
1440.2.k.d 4
1440.2.k.e 4
1440.2.k.f 6
1440.2.m $$\chi_{1440}(719, \cdot)$$ 1440.2.m.a 4 1
1440.2.m.b 4
1440.2.m.c 16
1440.2.o $$\chi_{1440}(1439, \cdot)$$ 1440.2.o.a 12 1
1440.2.o.b 12
1440.2.q $$\chi_{1440}(481, \cdot)$$ 1440.2.q.a 2 2
1440.2.q.b 2
1440.2.q.c 2
1440.2.q.d 2
1440.2.q.e 2
1440.2.q.f 2
1440.2.q.g 2
1440.2.q.h 2
1440.2.q.i 8
1440.2.q.j 8
1440.2.q.k 8
1440.2.q.l 8
1440.2.q.m 8
1440.2.q.n 8
1440.2.q.o 10
1440.2.q.p 10
1440.2.q.q 12
1440.2.t $$\chi_{1440}(361, \cdot)$$ None 0 2
1440.2.u $$\chi_{1440}(359, \cdot)$$ None 0 2
1440.2.w $$\chi_{1440}(737, \cdot)$$ 1440.2.w.a 4 2
1440.2.w.b 4
1440.2.w.c 4
1440.2.w.d 4
1440.2.w.e 8
1440.2.w.f 12
1440.2.w.g 12
1440.2.x $$\chi_{1440}(127, \cdot)$$ 1440.2.x.a 2 2
1440.2.x.b 2
1440.2.x.c 2
1440.2.x.d 2
1440.2.x.e 2
1440.2.x.f 2
1440.2.x.g 2
1440.2.x.h 2
1440.2.x.i 2
1440.2.x.j 2
1440.2.x.k 4
1440.2.x.l 4
1440.2.x.m 4
1440.2.x.n 4
1440.2.x.o 4
1440.2.x.p 4
1440.2.x.q 8
1440.2.x.r 8
1440.2.z $$\chi_{1440}(343, \cdot)$$ None 0 2
1440.2.bc $$\chi_{1440}(233, \cdot)$$ None 0 2
1440.2.bd $$\chi_{1440}(1063, \cdot)$$ None 0 2
1440.2.bg $$\chi_{1440}(953, \cdot)$$ None 0 2
1440.2.bi $$\chi_{1440}(847, \cdot)$$ 1440.2.bi.a 4 2
1440.2.bi.b 4
1440.2.bi.c 8
1440.2.bi.d 16
1440.2.bi.e 24
1440.2.bj $$\chi_{1440}(17, \cdot)$$ 1440.2.bj.a 48 2
1440.2.bl $$\chi_{1440}(71, \cdot)$$ None 0 2
1440.2.bm $$\chi_{1440}(649, \cdot)$$ None 0 2
1440.2.br $$\chi_{1440}(479, \cdot)$$ n/a 144 2
1440.2.bt $$\chi_{1440}(239, \cdot)$$ n/a 136 2
1440.2.bv $$\chi_{1440}(241, \cdot)$$ 1440.2.bv.a 4 2
1440.2.bv.b 92
1440.2.bw $$\chi_{1440}(191, \cdot)$$ 1440.2.bw.a 48 2
1440.2.bw.b 48
1440.2.by $$\chi_{1440}(769, \cdot)$$ n/a 144 2
1440.2.ca $$\chi_{1440}(49, \cdot)$$ n/a 136 2
1440.2.cc $$\chi_{1440}(911, \cdot)$$ 1440.2.cc.a 48 2
1440.2.cc.b 48
1440.2.ce $$\chi_{1440}(307, \cdot)$$ n/a 472 4
1440.2.ch $$\chi_{1440}(197, \cdot)$$ n/a 384 4
1440.2.ci $$\chi_{1440}(179, \cdot)$$ n/a 384 4
1440.2.cl $$\chi_{1440}(181, \cdot)$$ n/a 320 4
1440.2.cn $$\chi_{1440}(251, \cdot)$$ n/a 256 4
1440.2.co $$\chi_{1440}(109, \cdot)$$ n/a 472 4
1440.2.cr $$\chi_{1440}(53, \cdot)$$ n/a 384 4
1440.2.cs $$\chi_{1440}(163, \cdot)$$ n/a 472 4
1440.2.cu $$\chi_{1440}(169, \cdot)$$ None 0 4
1440.2.cv $$\chi_{1440}(311, \cdot)$$ None 0 4
1440.2.cy $$\chi_{1440}(367, \cdot)$$ n/a 272 4
1440.2.db $$\chi_{1440}(113, \cdot)$$ n/a 272 4
1440.2.dc $$\chi_{1440}(137, \cdot)$$ None 0 4
1440.2.df $$\chi_{1440}(103, \cdot)$$ None 0 4
1440.2.dg $$\chi_{1440}(713, \cdot)$$ None 0 4
1440.2.dj $$\chi_{1440}(7, \cdot)$$ None 0 4
1440.2.dk $$\chi_{1440}(257, \cdot)$$ n/a 288 4
1440.2.dn $$\chi_{1440}(223, \cdot)$$ n/a 288 4
1440.2.dq $$\chi_{1440}(119, \cdot)$$ None 0 4
1440.2.dr $$\chi_{1440}(121, \cdot)$$ None 0 4
1440.2.dt $$\chi_{1440}(187, \cdot)$$ n/a 2272 8
1440.2.du $$\chi_{1440}(77, \cdot)$$ n/a 2272 8
1440.2.dw $$\chi_{1440}(61, \cdot)$$ n/a 1536 8
1440.2.dz $$\chi_{1440}(59, \cdot)$$ n/a 2272 8
1440.2.eb $$\chi_{1440}(229, \cdot)$$ n/a 2272 8
1440.2.ec $$\chi_{1440}(11, \cdot)$$ n/a 1536 8
1440.2.ee $$\chi_{1440}(173, \cdot)$$ n/a 2272 8
1440.2.eh $$\chi_{1440}(43, \cdot)$$ n/a 2272 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1440))$$ into lower level spaces

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