# Properties

 Label 560.5 Level 560 Weight 5 Dimension 18082 Nonzero newspaces 28 Sturm bound 92160 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$28$$ Sturm bound: $$92160$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(560))$$.

Total New Old
Modular forms 37536 18350 19186
Cusp forms 36192 18082 18110
Eisenstein series 1344 268 1076

## Trace form

 $$18082 q - 16 q^{2} - 14 q^{3} - 40 q^{4} + 43 q^{5} + 216 q^{6} - 20 q^{7} - 400 q^{8} - 894 q^{9} + O(q^{10})$$ $$18082 q - 16 q^{2} - 14 q^{3} - 40 q^{4} + 43 q^{5} + 216 q^{6} - 20 q^{7} - 400 q^{8} - 894 q^{9} - 220 q^{10} + 346 q^{11} - 1336 q^{12} + 920 q^{13} + 72 q^{14} + 1302 q^{15} - 712 q^{16} - 82 q^{17} + 5552 q^{18} - 5322 q^{19} + 3780 q^{20} + 786 q^{21} + 3568 q^{22} + 6026 q^{23} - 7496 q^{24} - 2845 q^{25} - 13704 q^{26} - 4412 q^{27} - 5536 q^{28} - 484 q^{29} + 4596 q^{30} - 8606 q^{31} + 4424 q^{32} - 6046 q^{33} + 2504 q^{34} - 2137 q^{35} + 21568 q^{36} - 8034 q^{37} + 5864 q^{38} + 20740 q^{39} + 2332 q^{40} + 11264 q^{41} + 14960 q^{42} + 24064 q^{43} + 11576 q^{44} + 23266 q^{45} + 5344 q^{46} - 17286 q^{47} - 34136 q^{48} - 86438 q^{49} + 5104 q^{50} - 26190 q^{51} - 33840 q^{52} - 16770 q^{53} - 13560 q^{54} - 8012 q^{55} + 4688 q^{56} + 11444 q^{57} - 27904 q^{58} + 8438 q^{59} + 15844 q^{60} + 31830 q^{61} + 67504 q^{62} + 37756 q^{63} + 64424 q^{64} - 7448 q^{65} + 88024 q^{66} - 8238 q^{67} + 39120 q^{68} - 31960 q^{69} - 7700 q^{70} - 42532 q^{71} - 9544 q^{72} - 3730 q^{73} + 13112 q^{74} - 39599 q^{75} - 41112 q^{76} + 32710 q^{77} + 15136 q^{78} + 47694 q^{79} - 22692 q^{80} - 6404 q^{81} - 10600 q^{82} + 16312 q^{83} - 69448 q^{84} + 18850 q^{85} - 129432 q^{86} - 1880 q^{87} - 121336 q^{88} + 2730 q^{89} - 182164 q^{90} + 18412 q^{91} - 163256 q^{92} + 26970 q^{93} - 183368 q^{94} - 25595 q^{95} + 116488 q^{96} - 5880 q^{97} + 119304 q^{98} - 35724 q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(560))$$

We only show spaces with odd 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
560.5.c $$\chi_{560}(489, \cdot)$$ None 0 1
560.5.d $$\chi_{560}(351, \cdot)$$ 560.5.d.a 16 1
560.5.d.b 32
560.5.f $$\chi_{560}(321, \cdot)$$ 560.5.f.a 8 1
560.5.f.b 12
560.5.f.c 12
560.5.f.d 32
560.5.i $$\chi_{560}(519, \cdot)$$ None 0 1
560.5.j $$\chi_{560}(239, \cdot)$$ 560.5.j.a 24 1
560.5.j.b 48
560.5.m $$\chi_{560}(41, \cdot)$$ None 0 1
560.5.o $$\chi_{560}(71, \cdot)$$ None 0 1
560.5.p $$\chi_{560}(209, \cdot)$$ 560.5.p.a 1 1
560.5.p.b 1
560.5.p.c 2
560.5.p.d 2
560.5.p.e 2
560.5.p.f 2
560.5.p.g 8
560.5.p.h 12
560.5.p.i 16
560.5.p.j 48
560.5.s $$\chi_{560}(197, \cdot)$$ n/a 576 2
560.5.u $$\chi_{560}(27, \cdot)$$ n/a 760 2
560.5.v $$\chi_{560}(223, \cdot)$$ n/a 192 2
560.5.y $$\chi_{560}(57, \cdot)$$ None 0 2
560.5.z $$\chi_{560}(181, \cdot)$$ n/a 512 2
560.5.ba $$\chi_{560}(99, \cdot)$$ n/a 576 2
560.5.bf $$\chi_{560}(69, \cdot)$$ n/a 760 2
560.5.bg $$\chi_{560}(211, \cdot)$$ n/a 384 2
560.5.bh $$\chi_{560}(113, \cdot)$$ n/a 144 2
560.5.bk $$\chi_{560}(167, \cdot)$$ None 0 2
560.5.bm $$\chi_{560}(307, \cdot)$$ n/a 760 2
560.5.bo $$\chi_{560}(477, \cdot)$$ n/a 576 2
560.5.bp $$\chi_{560}(151, \cdot)$$ None 0 2
560.5.br $$\chi_{560}(129, \cdot)$$ n/a 188 2
560.5.bt $$\chi_{560}(79, \cdot)$$ n/a 192 2
560.5.bu $$\chi_{560}(201, \cdot)$$ None 0 2
560.5.bx $$\chi_{560}(241, \cdot)$$ n/a 128 2
560.5.by $$\chi_{560}(39, \cdot)$$ None 0 2
560.5.ca $$\chi_{560}(89, \cdot)$$ None 0 2
560.5.cd $$\chi_{560}(191, \cdot)$$ n/a 128 2
560.5.ce $$\chi_{560}(227, \cdot)$$ n/a 1520 4
560.5.cg $$\chi_{560}(53, \cdot)$$ n/a 1520 4
560.5.cj $$\chi_{560}(87, \cdot)$$ None 0 4
560.5.ck $$\chi_{560}(177, \cdot)$$ n/a 376 4
560.5.cm $$\chi_{560}(11, \cdot)$$ n/a 1024 4
560.5.cn $$\chi_{560}(229, \cdot)$$ n/a 1520 4
560.5.cs $$\chi_{560}(179, \cdot)$$ n/a 1520 4
560.5.ct $$\chi_{560}(61, \cdot)$$ n/a 1024 4
560.5.cv $$\chi_{560}(137, \cdot)$$ None 0 4
560.5.cw $$\chi_{560}(47, \cdot)$$ n/a 384 4
560.5.cy $$\chi_{560}(37, \cdot)$$ n/a 1520 4
560.5.da $$\chi_{560}(3, \cdot)$$ n/a 1520 4

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

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(560))$$ into lower level spaces

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