# Properties

 Label 1080.6 Level 1080 Weight 6 Dimension 63168 Nonzero newspaces 27 Sturm bound 373248 Trace bound 22

## Defining parameters

 Level: $$N$$ = $$1080 = 2^{3} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$27$$ Sturm bound: $$373248$$ Trace bound: $$22$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(1080))$$.

Total New Old
Modular forms 156960 63552 93408
Cusp forms 154080 63168 90912
Eisenstein series 2880 384 2496

## Trace form

 $$63168 q - 16 q^{2} - 24 q^{3} - 28 q^{4} + 50 q^{5} - 72 q^{6} + 20 q^{7} + 836 q^{8} - 48 q^{9} + O(q^{10})$$ $$63168 q - 16 q^{2} - 24 q^{3} - 28 q^{4} + 50 q^{5} - 72 q^{6} + 20 q^{7} + 836 q^{8} - 48 q^{9} - 610 q^{10} - 3336 q^{11} - 24 q^{12} + 3068 q^{13} + 2132 q^{14} - 768 q^{15} + 7460 q^{16} - 8580 q^{17} - 24 q^{18} - 332 q^{19} - 2898 q^{20} + 7464 q^{21} + 10284 q^{22} + 18924 q^{23} + 2892 q^{24} + 14830 q^{25} + 56724 q^{26} - 28722 q^{27} - 76232 q^{28} - 57852 q^{29} - 34836 q^{30} + 4116 q^{31} + 44364 q^{32} + 12714 q^{33} + 120452 q^{34} + 88594 q^{35} + 142608 q^{36} + 55996 q^{37} + 65500 q^{38} - 6864 q^{39} - 64206 q^{40} + 71652 q^{41} - 241104 q^{42} - 76996 q^{43} - 310644 q^{44} - 117234 q^{45} + 125604 q^{46} + 184240 q^{47} + 235020 q^{48} - 148106 q^{49} - 153294 q^{50} + 171264 q^{51} - 111668 q^{52} + 145216 q^{53} - 24 q^{54} - 24766 q^{55} - 397148 q^{56} + 202002 q^{57} - 105644 q^{58} - 169370 q^{59} + 212304 q^{60} - 142996 q^{61} + 1312020 q^{62} - 838776 q^{63} + 205772 q^{64} - 216222 q^{65} - 5652 q^{66} - 9068 q^{67} - 1206468 q^{68} + 699648 q^{69} - 769926 q^{70} + 1368820 q^{71} - 834816 q^{72} + 430348 q^{73} - 490748 q^{74} + 188382 q^{75} + 196324 q^{76} - 643376 q^{77} + 459180 q^{78} - 816540 q^{79} + 874778 q^{80} - 792312 q^{81} + 42256 q^{82} - 2192188 q^{83} + 920148 q^{84} + 15204 q^{85} - 726468 q^{86} + 845244 q^{87} - 892452 q^{88} + 870678 q^{89} - 1495974 q^{90} + 770904 q^{91} + 1348820 q^{92} + 868320 q^{93} + 182524 q^{94} + 1536936 q^{95} + 3429120 q^{96} - 307964 q^{97} + 2997356 q^{98} + 510012 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(1080))$$

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
1080.6.a $$\chi_{1080}(1, \cdot)$$ 1080.6.a.a 1 1
1080.6.a.b 1
1080.6.a.c 2
1080.6.a.d 2
1080.6.a.e 3
1080.6.a.f 3
1080.6.a.g 3
1080.6.a.h 3
1080.6.a.i 5
1080.6.a.j 5
1080.6.a.k 5
1080.6.a.l 5
1080.6.a.m 5
1080.6.a.n 5
1080.6.a.o 5
1080.6.a.p 5
1080.6.a.q 5
1080.6.a.r 5
1080.6.a.s 6
1080.6.a.t 6
1080.6.b $$\chi_{1080}(971, \cdot)$$ n/a 320 1
1080.6.d $$\chi_{1080}(109, \cdot)$$ n/a 480 1
1080.6.f $$\chi_{1080}(649, \cdot)$$ n/a 120 1
1080.6.h $$\chi_{1080}(431, \cdot)$$ None 0 1
1080.6.k $$\chi_{1080}(541, \cdot)$$ n/a 320 1
1080.6.m $$\chi_{1080}(539, \cdot)$$ n/a 480 1
1080.6.o $$\chi_{1080}(1079, \cdot)$$ None 0 1
1080.6.q $$\chi_{1080}(361, \cdot)$$ n/a 120 2
1080.6.s $$\chi_{1080}(377, \cdot)$$ n/a 240 2
1080.6.t $$\chi_{1080}(487, \cdot)$$ None 0 2
1080.6.w $$\chi_{1080}(163, \cdot)$$ n/a 960 2
1080.6.x $$\chi_{1080}(53, \cdot)$$ n/a 960 2
1080.6.bb $$\chi_{1080}(359, \cdot)$$ None 0 2
1080.6.bd $$\chi_{1080}(179, \cdot)$$ n/a 712 2
1080.6.bf $$\chi_{1080}(181, \cdot)$$ n/a 480 2
1080.6.bg $$\chi_{1080}(71, \cdot)$$ None 0 2
1080.6.bi $$\chi_{1080}(289, \cdot)$$ n/a 180 2
1080.6.bk $$\chi_{1080}(469, \cdot)$$ n/a 712 2
1080.6.bm $$\chi_{1080}(251, \cdot)$$ n/a 480 2
1080.6.bo $$\chi_{1080}(121, \cdot)$$ n/a 1080 6
1080.6.bp $$\chi_{1080}(307, \cdot)$$ n/a 1424 4
1080.6.bs $$\chi_{1080}(197, \cdot)$$ n/a 1424 4
1080.6.bt $$\chi_{1080}(17, \cdot)$$ n/a 360 4
1080.6.bw $$\chi_{1080}(127, \cdot)$$ None 0 4
1080.6.bx $$\chi_{1080}(59, \cdot)$$ n/a 6456 6
1080.6.cc $$\chi_{1080}(61, \cdot)$$ n/a 4320 6
1080.6.cd $$\chi_{1080}(119, \cdot)$$ None 0 6
1080.6.cg $$\chi_{1080}(49, \cdot)$$ n/a 1620 6
1080.6.ch $$\chi_{1080}(11, \cdot)$$ n/a 4320 6
1080.6.ci $$\chi_{1080}(191, \cdot)$$ None 0 6
1080.6.cj $$\chi_{1080}(229, \cdot)$$ n/a 6456 6
1080.6.co $$\chi_{1080}(77, \cdot)$$ n/a 12912 12
1080.6.cp $$\chi_{1080}(7, \cdot)$$ None 0 12
1080.6.cs $$\chi_{1080}(113, \cdot)$$ n/a 3240 12
1080.6.ct $$\chi_{1080}(43, \cdot)$$ n/a 12912 12

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(1080))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(1080)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 16}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 16}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 18}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 16}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 9}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 2}$$