# Properties

 Label 6480.2 Level 6480 Weight 2 Dimension 454680 Nonzero newspaces 56 Sturm bound 4478976

## Defining parameters

 Level: $$N$$ = $$6480 = 2^{4} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$4478976$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6480))$$.

Total New Old
Modular forms 1131840 457704 674136
Cusp forms 1107649 454680 652969
Eisenstein series 24191 3024 21167

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6480))$$

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
6480.2.a $$\chi_{6480}(1, \cdot)$$ 6480.2.a.a 1 1
6480.2.a.b 1
6480.2.a.c 1
6480.2.a.d 1
6480.2.a.e 1
6480.2.a.f 1
6480.2.a.g 1
6480.2.a.h 1
6480.2.a.i 1
6480.2.a.j 1
6480.2.a.k 1
6480.2.a.l 1
6480.2.a.m 1
6480.2.a.n 1
6480.2.a.o 1
6480.2.a.p 1
6480.2.a.q 1
6480.2.a.r 1
6480.2.a.s 1
6480.2.a.t 1
6480.2.a.u 1
6480.2.a.v 1
6480.2.a.w 1
6480.2.a.x 1
6480.2.a.y 1
6480.2.a.z 1
6480.2.a.ba 2
6480.2.a.bb 2
6480.2.a.bc 2
6480.2.a.bd 2
6480.2.a.be 2
6480.2.a.bf 2
6480.2.a.bg 2
6480.2.a.bh 2
6480.2.a.bi 2
6480.2.a.bj 2
6480.2.a.bk 2
6480.2.a.bl 2
6480.2.a.bm 2
6480.2.a.bn 2
6480.2.a.bo 2
6480.2.a.bp 2
6480.2.a.bq 2
6480.2.a.br 2
6480.2.a.bs 3
6480.2.a.bt 3
6480.2.a.bu 3
6480.2.a.bv 3
6480.2.a.bw 3
6480.2.a.bx 3
6480.2.a.by 4
6480.2.a.bz 4
6480.2.a.ca 4
6480.2.a.cb 4
6480.2.b $$\chi_{6480}(5831, \cdot)$$ None 0 1
6480.2.d $$\chi_{6480}(649, \cdot)$$ None 0 1
6480.2.f $$\chi_{6480}(3889, \cdot)$$ n/a 140 1
6480.2.h $$\chi_{6480}(2591, \cdot)$$ 6480.2.h.a 16 1
6480.2.h.b 16
6480.2.h.c 16
6480.2.h.d 16
6480.2.h.e 16
6480.2.h.f 16
6480.2.k $$\chi_{6480}(3241, \cdot)$$ None 0 1
6480.2.m $$\chi_{6480}(3239, \cdot)$$ None 0 1
6480.2.o $$\chi_{6480}(6479, \cdot)$$ n/a 144 1
6480.2.q $$\chi_{6480}(2161, \cdot)$$ n/a 192 2
6480.2.t $$\chi_{6480}(1621, \cdot)$$ n/a 768 2
6480.2.u $$\chi_{6480}(1619, \cdot)$$ n/a 1136 2
6480.2.w $$\chi_{6480}(1457, \cdot)$$ n/a 280 2
6480.2.x $$\chi_{6480}(3727, \cdot)$$ n/a 288 2
6480.2.z $$\chi_{6480}(163, \cdot)$$ n/a 1136 2
6480.2.bc $$\chi_{6480}(1133, \cdot)$$ n/a 1136 2
6480.2.bd $$\chi_{6480}(3403, \cdot)$$ n/a 1136 2
6480.2.bg $$\chi_{6480}(4373, \cdot)$$ n/a 1136 2
6480.2.bi $$\chi_{6480}(487, \cdot)$$ None 0 2
6480.2.bj $$\chi_{6480}(4697, \cdot)$$ None 0 2
6480.2.bl $$\chi_{6480}(971, \cdot)$$ n/a 768 2
6480.2.bm $$\chi_{6480}(2269, \cdot)$$ n/a 1136 2
6480.2.br $$\chi_{6480}(2159, \cdot)$$ n/a 288 2
6480.2.bt $$\chi_{6480}(1079, \cdot)$$ None 0 2
6480.2.bv $$\chi_{6480}(1081, \cdot)$$ None 0 2
6480.2.bw $$\chi_{6480}(431, \cdot)$$ n/a 192 2
6480.2.by $$\chi_{6480}(1729, \cdot)$$ n/a 284 2
6480.2.ca $$\chi_{6480}(2809, \cdot)$$ None 0 2
6480.2.cc $$\chi_{6480}(1511, \cdot)$$ None 0 2
6480.2.ce $$\chi_{6480}(721, \cdot)$$ n/a 432 6
6480.2.cf $$\chi_{6480}(109, \cdot)$$ n/a 2288 4
6480.2.cg $$\chi_{6480}(2051, \cdot)$$ n/a 1536 4
6480.2.cj $$\chi_{6480}(2647, \cdot)$$ None 0 4
6480.2.cm $$\chi_{6480}(377, \cdot)$$ None 0 4
6480.2.cn $$\chi_{6480}(53, \cdot)$$ n/a 2288 4
6480.2.cq $$\chi_{6480}(1027, \cdot)$$ n/a 2288 4
6480.2.cr $$\chi_{6480}(917, \cdot)$$ n/a 2288 4
6480.2.cu $$\chi_{6480}(2323, \cdot)$$ n/a 2288 4
6480.2.cv $$\chi_{6480}(593, \cdot)$$ n/a 568 4
6480.2.cy $$\chi_{6480}(703, \cdot)$$ n/a 576 4
6480.2.db $$\chi_{6480}(539, \cdot)$$ n/a 2288 4
6480.2.dc $$\chi_{6480}(541, \cdot)$$ n/a 1536 4
6480.2.dd $$\chi_{6480}(359, \cdot)$$ None 0 6
6480.2.di $$\chi_{6480}(361, \cdot)$$ None 0 6
6480.2.dj $$\chi_{6480}(719, \cdot)$$ n/a 648 6
6480.2.dm $$\chi_{6480}(289, \cdot)$$ n/a 636 6
6480.2.dn $$\chi_{6480}(71, \cdot)$$ None 0 6
6480.2.do $$\chi_{6480}(1151, \cdot)$$ n/a 432 6
6480.2.dp $$\chi_{6480}(1369, \cdot)$$ None 0 6
6480.2.ds $$\chi_{6480}(241, \cdot)$$ n/a 3888 18
6480.2.dv $$\chi_{6480}(179, \cdot)$$ n/a 5136 12
6480.2.dw $$\chi_{6480}(181, \cdot)$$ n/a 3456 12
6480.2.dz $$\chi_{6480}(233, \cdot)$$ None 0 12
6480.2.ea $$\chi_{6480}(127, \cdot)$$ n/a 1296 12
6480.2.eb $$\chi_{6480}(307, \cdot)$$ n/a 5136 12
6480.2.ed $$\chi_{6480}(557, \cdot)$$ n/a 5136 12
6480.2.ef $$\chi_{6480}(197, \cdot)$$ n/a 5136 12
6480.2.eh $$\chi_{6480}(667, \cdot)$$ n/a 5136 12
6480.2.el $$\chi_{6480}(17, \cdot)$$ n/a 1272 12
6480.2.em $$\chi_{6480}(343, \cdot)$$ None 0 12
6480.2.ep $$\chi_{6480}(469, \cdot)$$ n/a 5136 12
6480.2.eq $$\chi_{6480}(251, \cdot)$$ n/a 3456 12
6480.2.et $$\chi_{6480}(169, \cdot)$$ None 0 18
6480.2.eu $$\chi_{6480}(239, \cdot)$$ n/a 5832 18
6480.2.ew $$\chi_{6480}(311, \cdot)$$ None 0 18
6480.2.ey $$\chi_{6480}(191, \cdot)$$ n/a 3888 18
6480.2.fa $$\chi_{6480}(119, \cdot)$$ None 0 18
6480.2.fd $$\chi_{6480}(49, \cdot)$$ n/a 5796 18
6480.2.ff $$\chi_{6480}(121, \cdot)$$ None 0 18
6480.2.fh $$\chi_{6480}(187, \cdot)$$ n/a 46512 36
6480.2.fi $$\chi_{6480}(77, \cdot)$$ n/a 46512 36
6480.2.fk $$\chi_{6480}(137, \cdot)$$ None 0 36
6480.2.fn $$\chi_{6480}(7, \cdot)$$ None 0 36
6480.2.fp $$\chi_{6480}(59, \cdot)$$ n/a 46512 36
6480.2.fr $$\chi_{6480}(11, \cdot)$$ n/a 31104 36
6480.2.fs $$\chi_{6480}(229, \cdot)$$ n/a 46512 36
6480.2.fu $$\chi_{6480}(61, \cdot)$$ n/a 31104 36
6480.2.fw $$\chi_{6480}(113, \cdot)$$ n/a 11592 36
6480.2.fz $$\chi_{6480}(223, \cdot)$$ n/a 11664 36
6480.2.ga $$\chi_{6480}(173, \cdot)$$ n/a 46512 36
6480.2.gd $$\chi_{6480}(43, \cdot)$$ n/a 46512 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6480))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6480)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(405))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(432))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(648))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(720))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(810))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1080))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1296))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1620))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2160))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3240))$$$$^{\oplus 2}$$