# Properties

 Label 1080.1 Level 1080 Weight 1 Dimension 28 Nonzero newspaces 4 Newform subspaces 10 Sturm bound 62208 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1080 = 2^{3} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$10$$ Sturm bound: $$62208$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1080))$$.

Total New Old
Modular forms 1606 220 1386
Cusp forms 166 28 138
Eisenstein series 1440 192 1248

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 24 0 4 0

## Trace form

 $$28 q + 4 q^{7} + O(q^{10})$$ $$28 q + 4 q^{7} - 6 q^{10} - 4 q^{16} + 8 q^{19} - 4 q^{22} + 6 q^{25} + 4 q^{28} + 4 q^{31} - 16 q^{34} - 6 q^{40} - 4 q^{49} - 2 q^{55} - 8 q^{58} - 4 q^{61} - 2 q^{70} - 4 q^{73} + 4 q^{76} - 4 q^{79} - 4 q^{88} - 4 q^{91} - 8 q^{94} + 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1080))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1080.1.c $$\chi_{1080}(809, \cdot)$$ 1080.1.c.a 4 1
1080.1.e $$\chi_{1080}(271, \cdot)$$ None 0 1
1080.1.g $$\chi_{1080}(811, \cdot)$$ None 0 1
1080.1.i $$\chi_{1080}(269, \cdot)$$ 1080.1.i.a 1 1
1080.1.i.b 1
1080.1.i.c 1
1080.1.i.d 1
1080.1.i.e 4
1080.1.i.f 4
1080.1.j $$\chi_{1080}(919, \cdot)$$ None 0 1
1080.1.l $$\chi_{1080}(161, \cdot)$$ None 0 1
1080.1.n $$\chi_{1080}(701, \cdot)$$ None 0 1
1080.1.p $$\chi_{1080}(379, \cdot)$$ 1080.1.p.a 2 1
1080.1.p.b 2
1080.1.r $$\chi_{1080}(107, \cdot)$$ None 0 2
1080.1.u $$\chi_{1080}(757, \cdot)$$ 1080.1.u.a 8 2
1080.1.v $$\chi_{1080}(217, \cdot)$$ None 0 2
1080.1.y $$\chi_{1080}(647, \cdot)$$ None 0 2
1080.1.z $$\chi_{1080}(19, \cdot)$$ None 0 2
1080.1.ba $$\chi_{1080}(341, \cdot)$$ None 0 2
1080.1.bc $$\chi_{1080}(521, \cdot)$$ None 0 2
1080.1.be $$\chi_{1080}(199, \cdot)$$ None 0 2
1080.1.bh $$\chi_{1080}(629, \cdot)$$ None 0 2
1080.1.bj $$\chi_{1080}(91, \cdot)$$ None 0 2
1080.1.bl $$\chi_{1080}(631, \cdot)$$ None 0 2
1080.1.bn $$\chi_{1080}(89, \cdot)$$ None 0 2
1080.1.bq $$\chi_{1080}(73, \cdot)$$ None 0 4
1080.1.br $$\chi_{1080}(143, \cdot)$$ None 0 4
1080.1.bu $$\chi_{1080}(467, \cdot)$$ None 0 4
1080.1.bv $$\chi_{1080}(37, \cdot)$$ None 0 4
1080.1.by $$\chi_{1080}(211, \cdot)$$ None 0 6
1080.1.bz $$\chi_{1080}(209, \cdot)$$ None 0 6
1080.1.ca $$\chi_{1080}(29, \cdot)$$ None 0 6
1080.1.cb $$\chi_{1080}(31, \cdot)$$ None 0 6
1080.1.ce $$\chi_{1080}(41, \cdot)$$ None 0 6
1080.1.cf $$\chi_{1080}(139, \cdot)$$ None 0 6
1080.1.ck $$\chi_{1080}(79, \cdot)$$ None 0 6
1080.1.cl $$\chi_{1080}(101, \cdot)$$ None 0 6
1080.1.cm $$\chi_{1080}(23, \cdot)$$ None 0 12
1080.1.cn $$\chi_{1080}(13, \cdot)$$ None 0 12
1080.1.cq $$\chi_{1080}(83, \cdot)$$ None 0 12
1080.1.cr $$\chi_{1080}(97, \cdot)$$ None 0 12

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1080))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1080)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 32}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 16}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 16}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 18}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 16}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 9}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1080))$$$$^{\oplus 1}$$