# Properties

 Label 1440.4 Level 1440 Weight 4 Dimension 67446 Nonzero newspaces 40 Sturm bound 442368 Trace bound 53

## Defining parameters

 Level: $$N$$ = $$1440 = 2^{5} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$40$$ Sturm bound: $$442368$$ Trace bound: $$53$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1440))$$.

Total New Old
Modular forms 167936 67986 99950
Cusp forms 163840 67446 96394
Eisenstein series 4096 540 3556

## Trace form

 $$67446 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 38 q^{5} - 96 q^{6} - 48 q^{7} - 24 q^{8} - 48 q^{9} + O(q^{10})$$ $$67446 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 38 q^{5} - 96 q^{6} - 48 q^{7} - 24 q^{8} - 48 q^{9} - 228 q^{10} - 60 q^{11} - 32 q^{12} + 212 q^{13} + 392 q^{14} - 90 q^{15} + 528 q^{16} - 260 q^{17} - 32 q^{18} + 40 q^{19} - 116 q^{20} + 448 q^{21} - 416 q^{22} - 168 q^{23} - 32 q^{24} + 406 q^{25} - 112 q^{26} + 240 q^{27} - 832 q^{28} - 644 q^{29} + 16 q^{30} + 756 q^{31} - 1264 q^{32} - 936 q^{33} - 1088 q^{34} + 888 q^{35} + 3984 q^{36} + 3612 q^{37} + 7640 q^{38} + 468 q^{39} + 1648 q^{40} - 468 q^{41} - 2752 q^{42} - 2496 q^{43} - 8264 q^{44} - 2016 q^{45} - 8856 q^{46} - 2808 q^{47} - 9808 q^{48} - 5258 q^{49} - 5004 q^{50} - 1256 q^{51} - 1896 q^{52} - 5332 q^{53} - 912 q^{54} - 840 q^{55} + 5536 q^{56} + 7152 q^{57} + 9696 q^{58} + 3356 q^{59} + 6056 q^{60} + 9188 q^{61} + 8592 q^{62} + 1428 q^{63} - 2256 q^{64} + 2448 q^{65} - 96 q^{66} - 616 q^{67} + 2416 q^{68} - 8352 q^{69} + 144 q^{70} - 4992 q^{71} - 32 q^{72} + 5644 q^{73} - 1704 q^{74} - 3286 q^{75} + 1592 q^{76} - 10904 q^{77} - 10160 q^{78} + 23780 q^{79} - 20928 q^{80} + 6064 q^{81} - 26792 q^{82} + 19256 q^{83} - 8320 q^{84} - 5548 q^{85} - 880 q^{86} + 1756 q^{87} + 8720 q^{88} + 1220 q^{89} + 9312 q^{90} - 30008 q^{91} + 41216 q^{92} - 32 q^{93} + 24928 q^{94} - 20024 q^{95} + 25744 q^{96} - 9428 q^{97} + 38816 q^{98} - 23668 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1440))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1440.4.a $$\chi_{1440}(1, \cdot)$$ 1440.4.a.a 1 1
1440.4.a.b 1
1440.4.a.c 1
1440.4.a.d 1
1440.4.a.e 1
1440.4.a.f 1
1440.4.a.g 1
1440.4.a.h 1
1440.4.a.i 1
1440.4.a.j 1
1440.4.a.k 1
1440.4.a.l 1
1440.4.a.m 1
1440.4.a.n 1
1440.4.a.o 1
1440.4.a.p 1
1440.4.a.q 1
1440.4.a.r 1
1440.4.a.s 2
1440.4.a.t 2
1440.4.a.u 2
1440.4.a.v 2
1440.4.a.w 2
1440.4.a.x 2
1440.4.a.y 2
1440.4.a.z 2
1440.4.a.ba 2
1440.4.a.bb 2
1440.4.a.bc 2
1440.4.a.bd 2
1440.4.a.be 2
1440.4.a.bf 2
1440.4.a.bg 2
1440.4.a.bh 3
1440.4.a.bi 3
1440.4.a.bj 3
1440.4.a.bk 3
1440.4.b $$\chi_{1440}(431, \cdot)$$ 1440.4.b.a 24 1
1440.4.b.b 24
1440.4.d $$\chi_{1440}(1009, \cdot)$$ 1440.4.d.a 4 1
1440.4.d.b 4
1440.4.d.c 4
1440.4.d.d 16
1440.4.d.e 18
1440.4.d.f 18
1440.4.d.g 24
1440.4.f $$\chi_{1440}(289, \cdot)$$ 1440.4.f.a 2 1
1440.4.f.b 2
1440.4.f.c 2
1440.4.f.d 2
1440.4.f.e 2
1440.4.f.f 4
1440.4.f.g 4
1440.4.f.h 4
1440.4.f.i 6
1440.4.f.j 6
1440.4.f.k 8
1440.4.f.l 8
1440.4.f.m 8
1440.4.f.n 16
1440.4.f.o 16
1440.4.h $$\chi_{1440}(1151, \cdot)$$ 1440.4.h.a 12 1
1440.4.h.b 12
1440.4.h.c 12
1440.4.h.d 12
1440.4.k $$\chi_{1440}(721, \cdot)$$ 1440.4.k.a 2 1
1440.4.k.b 8
1440.4.k.c 12
1440.4.k.d 14
1440.4.k.e 24
1440.4.m $$\chi_{1440}(719, \cdot)$$ 1440.4.m.a 4 1
1440.4.m.b 4
1440.4.m.c 64
1440.4.o $$\chi_{1440}(1439, \cdot)$$ 1440.4.o.a 36 1
1440.4.o.b 36
1440.4.q $$\chi_{1440}(481, \cdot)$$ n/a 288 2
1440.4.t $$\chi_{1440}(361, \cdot)$$ None 0 2
1440.4.u $$\chi_{1440}(359, \cdot)$$ None 0 2
1440.4.w $$\chi_{1440}(737, \cdot)$$ n/a 144 2
1440.4.x $$\chi_{1440}(127, \cdot)$$ n/a 180 2
1440.4.z $$\chi_{1440}(343, \cdot)$$ None 0 2
1440.4.bc $$\chi_{1440}(233, \cdot)$$ None 0 2
1440.4.bd $$\chi_{1440}(1063, \cdot)$$ None 0 2
1440.4.bg $$\chi_{1440}(953, \cdot)$$ None 0 2
1440.4.bi $$\chi_{1440}(847, \cdot)$$ n/a 176 2
1440.4.bj $$\chi_{1440}(17, \cdot)$$ n/a 144 2
1440.4.bl $$\chi_{1440}(71, \cdot)$$ None 0 2
1440.4.bm $$\chi_{1440}(649, \cdot)$$ None 0 2
1440.4.br $$\chi_{1440}(479, \cdot)$$ n/a 432 2
1440.4.bt $$\chi_{1440}(239, \cdot)$$ n/a 424 2
1440.4.bv $$\chi_{1440}(241, \cdot)$$ n/a 288 2
1440.4.bw $$\chi_{1440}(191, \cdot)$$ n/a 288 2
1440.4.by $$\chi_{1440}(769, \cdot)$$ n/a 432 2
1440.4.ca $$\chi_{1440}(49, \cdot)$$ n/a 424 2
1440.4.cc $$\chi_{1440}(911, \cdot)$$ n/a 288 2
1440.4.ce $$\chi_{1440}(307, \cdot)$$ n/a 1432 4
1440.4.ch $$\chi_{1440}(197, \cdot)$$ n/a 1152 4
1440.4.ci $$\chi_{1440}(179, \cdot)$$ n/a 1152 4
1440.4.cl $$\chi_{1440}(181, \cdot)$$ n/a 960 4
1440.4.cn $$\chi_{1440}(251, \cdot)$$ n/a 768 4
1440.4.co $$\chi_{1440}(109, \cdot)$$ n/a 1432 4
1440.4.cr $$\chi_{1440}(53, \cdot)$$ n/a 1152 4
1440.4.cs $$\chi_{1440}(163, \cdot)$$ n/a 1432 4
1440.4.cu $$\chi_{1440}(169, \cdot)$$ None 0 4
1440.4.cv $$\chi_{1440}(311, \cdot)$$ None 0 4
1440.4.cy $$\chi_{1440}(367, \cdot)$$ n/a 848 4
1440.4.db $$\chi_{1440}(113, \cdot)$$ n/a 848 4
1440.4.dc $$\chi_{1440}(137, \cdot)$$ None 0 4
1440.4.df $$\chi_{1440}(103, \cdot)$$ None 0 4
1440.4.dg $$\chi_{1440}(713, \cdot)$$ None 0 4
1440.4.dj $$\chi_{1440}(7, \cdot)$$ None 0 4
1440.4.dk $$\chi_{1440}(257, \cdot)$$ n/a 864 4
1440.4.dn $$\chi_{1440}(223, \cdot)$$ n/a 864 4
1440.4.dq $$\chi_{1440}(119, \cdot)$$ None 0 4
1440.4.dr $$\chi_{1440}(121, \cdot)$$ None 0 4
1440.4.dt $$\chi_{1440}(187, \cdot)$$ n/a 6880 8
1440.4.du $$\chi_{1440}(77, \cdot)$$ n/a 6880 8
1440.4.dw $$\chi_{1440}(61, \cdot)$$ n/a 4608 8
1440.4.dz $$\chi_{1440}(59, \cdot)$$ n/a 6880 8
1440.4.eb $$\chi_{1440}(229, \cdot)$$ n/a 6880 8
1440.4.ec $$\chi_{1440}(11, \cdot)$$ n/a 4608 8
1440.4.ee $$\chi_{1440}(173, \cdot)$$ n/a 6880 8
1440.4.eh $$\chi_{1440}(43, \cdot)$$ n/a 6880 8

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1440))$$ into lower level spaces

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