# Properties

 Label 2880.1 Level 2880 Weight 1 Dimension 69 Nonzero newspaces 10 Newform subspaces 18 Sturm bound 442368 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$10$$ Newform subspaces: $$18$$ Sturm bound: $$442368$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2880))$$.

Total New Old
Modular forms 5132 663 4469
Cusp forms 524 69 455
Eisenstein series 4608 594 4014

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 69 0 0 0

## Trace form

 $$69 q - q^{5} + O(q^{10})$$ $$69 q - q^{5} - 2 q^{13} + 2 q^{17} - 4 q^{19} + 8 q^{21} - 11 q^{25} + 10 q^{29} + 2 q^{37} + 2 q^{41} - 7 q^{49} + 2 q^{53} + 10 q^{61} - 2 q^{65} - 2 q^{73} - 16 q^{76} + 16 q^{79} + 2 q^{85} - 10 q^{89} - 16 q^{94} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2880))$$

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
2880.1.c $$\chi_{2880}(449, \cdot)$$ 2880.1.c.a 4 1
2880.1.e $$\chi_{2880}(2431, \cdot)$$ None 0 1
2880.1.g $$\chi_{2880}(991, \cdot)$$ None 0 1
2880.1.i $$\chi_{2880}(1889, \cdot)$$ 2880.1.i.a 4 1
2880.1.i.b 4
2880.1.j $$\chi_{2880}(1279, \cdot)$$ 2880.1.j.a 1 1
2880.1.j.b 2
2880.1.l $$\chi_{2880}(1601, \cdot)$$ None 0 1
2880.1.n $$\chi_{2880}(161, \cdot)$$ None 0 1
2880.1.p $$\chi_{2880}(2719, \cdot)$$ 2880.1.p.a 2 1
2880.1.p.b 2
2880.1.r $$\chi_{2880}(559, \cdot)$$ 2880.1.r.a 4 2
2880.1.s $$\chi_{2880}(881, \cdot)$$ None 0 2
2880.1.v $$\chi_{2880}(287, \cdot)$$ None 0 2
2880.1.y $$\chi_{2880}(2017, \cdot)$$ None 0 2
2880.1.ba $$\chi_{2880}(1583, \cdot)$$ None 0 2
2880.1.bb $$\chi_{2880}(1873, \cdot)$$ None 0 2
2880.1.be $$\chi_{2880}(143, \cdot)$$ None 0 2
2880.1.bf $$\chi_{2880}(433, \cdot)$$ None 0 2
2880.1.bh $$\chi_{2880}(577, \cdot)$$ 2880.1.bh.a 2 2
2880.1.bh.b 2
2880.1.bh.c 2
2880.1.bk $$\chi_{2880}(1727, \cdot)$$ 2880.1.bk.a 4 2
2880.1.bk.b 4
2880.1.bn $$\chi_{2880}(1169, \cdot)$$ None 0 2
2880.1.bo $$\chi_{2880}(271, \cdot)$$ None 0 2
2880.1.bp $$\chi_{2880}(799, \cdot)$$ None 0 2
2880.1.bq $$\chi_{2880}(1121, \cdot)$$ None 0 2
2880.1.bs $$\chi_{2880}(641, \cdot)$$ None 0 2
2880.1.bu $$\chi_{2880}(319, \cdot)$$ 2880.1.bu.a 2 2
2880.1.bu.b 2
2880.1.bu.c 4
2880.1.bx $$\chi_{2880}(929, \cdot)$$ None 0 2
2880.1.bz $$\chi_{2880}(31, \cdot)$$ None 0 2
2880.1.cb $$\chi_{2880}(511, \cdot)$$ None 0 2
2880.1.cd $$\chi_{2880}(1409, \cdot)$$ 2880.1.cd.a 8 2
2880.1.cf $$\chi_{2880}(73, \cdot)$$ None 0 4
2880.1.cg $$\chi_{2880}(1223, \cdot)$$ None 0 4
2880.1.cj $$\chi_{2880}(631, \cdot)$$ None 0 4
2880.1.ck $$\chi_{2880}(89, \cdot)$$ None 0 4
2880.1.cm $$\chi_{2880}(199, \cdot)$$ None 0 4
2880.1.cp $$\chi_{2880}(521, \cdot)$$ None 0 4
2880.1.cq $$\chi_{2880}(503, \cdot)$$ None 0 4
2880.1.ct $$\chi_{2880}(793, \cdot)$$ None 0 4
2880.1.cw $$\chi_{2880}(751, \cdot)$$ None 0 4
2880.1.cx $$\chi_{2880}(209, \cdot)$$ None 0 4
2880.1.cz $$\chi_{2880}(193, \cdot)$$ None 0 4
2880.1.da $$\chi_{2880}(383, \cdot)$$ None 0 4
2880.1.dd $$\chi_{2880}(337, \cdot)$$ None 0 4
2880.1.de $$\chi_{2880}(47, \cdot)$$ None 0 4
2880.1.dh $$\chi_{2880}(817, \cdot)$$ None 0 4
2880.1.di $$\chi_{2880}(527, \cdot)$$ None 0 4
2880.1.dl $$\chi_{2880}(1247, \cdot)$$ None 0 4
2880.1.dm $$\chi_{2880}(97, \cdot)$$ None 0 4
2880.1.do $$\chi_{2880}(401, \cdot)$$ None 0 4
2880.1.dp $$\chi_{2880}(79, \cdot)$$ None 0 4
2880.1.ds $$\chi_{2880}(397, \cdot)$$ None 0 8
2880.1.dv $$\chi_{2880}(107, \cdot)$$ None 0 8
2880.1.dx $$\chi_{2880}(341, \cdot)$$ None 0 8
2880.1.dz $$\chi_{2880}(269, \cdot)$$ None 0 8
2880.1.ea $$\chi_{2880}(91, \cdot)$$ None 0 8
2880.1.ec $$\chi_{2880}(19, \cdot)$$ 2880.1.ec.a 16 8
2880.1.ee $$\chi_{2880}(37, \cdot)$$ None 0 8
2880.1.eh $$\chi_{2880}(467, \cdot)$$ None 0 8
2880.1.ei $$\chi_{2880}(313, \cdot)$$ None 0 8
2880.1.el $$\chi_{2880}(23, \cdot)$$ None 0 8
2880.1.en $$\chi_{2880}(329, \cdot)$$ None 0 8
2880.1.eo $$\chi_{2880}(151, \cdot)$$ None 0 8
2880.1.eq $$\chi_{2880}(41, \cdot)$$ None 0 8
2880.1.et $$\chi_{2880}(439, \cdot)$$ None 0 8
2880.1.ev $$\chi_{2880}(263, \cdot)$$ None 0 8
2880.1.ew $$\chi_{2880}(553, \cdot)$$ None 0 8
2880.1.ez $$\chi_{2880}(83, \cdot)$$ None 0 16
2880.1.fa $$\chi_{2880}(133, \cdot)$$ None 0 16
2880.1.fc $$\chi_{2880}(139, \cdot)$$ None 0 16
2880.1.fe $$\chi_{2880}(211, \cdot)$$ None 0 16
2880.1.fh $$\chi_{2880}(29, \cdot)$$ None 0 16
2880.1.fj $$\chi_{2880}(101, \cdot)$$ None 0 16
2880.1.fl $$\chi_{2880}(203, \cdot)$$ None 0 16
2880.1.fm $$\chi_{2880}(13, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2880))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2880)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 9}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(480))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(576))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(720))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(960))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1440))$$$$^{\oplus 2}$$