# Properties

 Label 1080.2 Level 1080 Weight 2 Dimension 12480 Nonzero newspaces 27 Sturm bound 124416 Trace bound 22

## Defining parameters

 Level: $$N$$ = $$1080 = 2^{3} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$27$$ Sturm bound: $$124416$$ Trace bound: $$22$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1080))$$.

Total New Old
Modular forms 32544 12864 19680
Cusp forms 29665 12480 17185
Eisenstein series 2879 384 2495

## Trace form

 $$12480 q - 16 q^{2} - 24 q^{3} - 28 q^{4} + 2 q^{5} - 72 q^{6} - 28 q^{7} - 28 q^{8} - 48 q^{9} + O(q^{10})$$ $$12480 q - 16 q^{2} - 24 q^{3} - 28 q^{4} + 2 q^{5} - 72 q^{6} - 28 q^{7} - 28 q^{8} - 48 q^{9} - 50 q^{10} - 72 q^{11} - 24 q^{12} - 20 q^{13} - 28 q^{14} - 48 q^{15} - 92 q^{16} - 84 q^{17} - 24 q^{18} - 60 q^{19} - 18 q^{20} - 24 q^{21} + 12 q^{22} - 84 q^{23} + 12 q^{24} - 106 q^{25} + 36 q^{26} + 6 q^{27} + 24 q^{28} + 36 q^{29} + 12 q^{30} - 60 q^{31} + 204 q^{32} - 30 q^{33} + 68 q^{34} + 34 q^{35} + 48 q^{36} + 44 q^{37} + 220 q^{38} + 48 q^{39} + 18 q^{40} - 60 q^{41} + 96 q^{42} + 44 q^{43} + 204 q^{44} + 54 q^{45} + 4 q^{46} + 160 q^{47} + 12 q^{48} - 98 q^{49} + 66 q^{50} + 48 q^{51} + 76 q^{52} + 64 q^{53} - 24 q^{54} - 22 q^{55} - 92 q^{56} + 42 q^{57} - 12 q^{58} + 238 q^{59} - 96 q^{60} + 28 q^{61} - 156 q^{62} + 168 q^{63} - 52 q^{64} + 66 q^{65} - 252 q^{66} + 132 q^{67} - 228 q^{68} + 96 q^{69} - 86 q^{70} + 244 q^{71} - 192 q^{72} + 28 q^{73} - 284 q^{74} + 102 q^{75} - 316 q^{76} + 208 q^{77} - 252 q^{78} + 148 q^{79} - 166 q^{80} - 24 q^{81} - 144 q^{82} + 308 q^{83} - 156 q^{84} + 84 q^{85} - 276 q^{86} + 108 q^{87} - 36 q^{88} + 126 q^{89} - 174 q^{90} + 88 q^{91} - 172 q^{92} + 28 q^{94} + 168 q^{95} - 384 q^{96} + 52 q^{97} - 316 q^{98} - 180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1080))$$

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
1080.2.a $$\chi_{1080}(1, \cdot)$$ 1080.2.a.a 1 1
1080.2.a.b 1
1080.2.a.c 1
1080.2.a.d 1
1080.2.a.e 1
1080.2.a.f 1
1080.2.a.g 1
1080.2.a.h 1
1080.2.a.i 1
1080.2.a.j 1
1080.2.a.k 1
1080.2.a.l 1
1080.2.a.m 2
1080.2.a.n 2
1080.2.b $$\chi_{1080}(971, \cdot)$$ 1080.2.b.a 16 1
1080.2.b.b 16
1080.2.b.c 16
1080.2.b.d 16
1080.2.d $$\chi_{1080}(109, \cdot)$$ 1080.2.d.a 4 1
1080.2.d.b 4
1080.2.d.c 4
1080.2.d.d 4
1080.2.d.e 4
1080.2.d.f 4
1080.2.d.g 16
1080.2.d.h 16
1080.2.d.i 20
1080.2.d.j 20
1080.2.f $$\chi_{1080}(649, \cdot)$$ 1080.2.f.a 2 1
1080.2.f.b 2
1080.2.f.c 2
1080.2.f.d 2
1080.2.f.e 4
1080.2.f.f 4
1080.2.f.g 8
1080.2.h $$\chi_{1080}(431, \cdot)$$ None 0 1
1080.2.k $$\chi_{1080}(541, \cdot)$$ 1080.2.k.a 12 1
1080.2.k.b 16
1080.2.k.c 16
1080.2.k.d 20
1080.2.m $$\chi_{1080}(539, \cdot)$$ 1080.2.m.a 8 1
1080.2.m.b 40
1080.2.m.c 48
1080.2.o $$\chi_{1080}(1079, \cdot)$$ None 0 1
1080.2.q $$\chi_{1080}(361, \cdot)$$ 1080.2.q.a 2 2
1080.2.q.b 4
1080.2.q.c 4
1080.2.q.d 6
1080.2.q.e 8
1080.2.s $$\chi_{1080}(377, \cdot)$$ 1080.2.s.a 24 2
1080.2.s.b 24
1080.2.t $$\chi_{1080}(487, \cdot)$$ None 0 2
1080.2.w $$\chi_{1080}(163, \cdot)$$ n/a 192 2
1080.2.x $$\chi_{1080}(53, \cdot)$$ n/a 192 2
1080.2.bb $$\chi_{1080}(359, \cdot)$$ None 0 2
1080.2.bd $$\chi_{1080}(179, \cdot)$$ n/a 136 2
1080.2.bf $$\chi_{1080}(181, \cdot)$$ 1080.2.bf.a 4 2
1080.2.bf.b 92
1080.2.bg $$\chi_{1080}(71, \cdot)$$ None 0 2
1080.2.bi $$\chi_{1080}(289, \cdot)$$ 1080.2.bi.a 4 2
1080.2.bi.b 32
1080.2.bk $$\chi_{1080}(469, \cdot)$$ n/a 136 2
1080.2.bm $$\chi_{1080}(251, \cdot)$$ 1080.2.bm.a 48 2
1080.2.bm.b 48
1080.2.bo $$\chi_{1080}(121, \cdot)$$ n/a 216 6
1080.2.bp $$\chi_{1080}(307, \cdot)$$ n/a 272 4
1080.2.bs $$\chi_{1080}(197, \cdot)$$ n/a 272 4
1080.2.bt $$\chi_{1080}(17, \cdot)$$ 1080.2.bt.a 72 4
1080.2.bw $$\chi_{1080}(127, \cdot)$$ None 0 4
1080.2.bx $$\chi_{1080}(59, \cdot)$$ n/a 1272 6
1080.2.cc $$\chi_{1080}(61, \cdot)$$ n/a 864 6
1080.2.cd $$\chi_{1080}(119, \cdot)$$ None 0 6
1080.2.cg $$\chi_{1080}(49, \cdot)$$ n/a 324 6
1080.2.ch $$\chi_{1080}(11, \cdot)$$ n/a 864 6
1080.2.ci $$\chi_{1080}(191, \cdot)$$ None 0 6
1080.2.cj $$\chi_{1080}(229, \cdot)$$ n/a 1272 6
1080.2.co $$\chi_{1080}(77, \cdot)$$ n/a 2544 12
1080.2.cp $$\chi_{1080}(7, \cdot)$$ None 0 12
1080.2.cs $$\chi_{1080}(113, \cdot)$$ n/a 648 12
1080.2.ct $$\chi_{1080}(43, \cdot)$$ n/a 2544 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1080))$$ into lower level spaces

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