# Properties

 Label 6080.2 Level 6080 Weight 2 Dimension 564828 Nonzero newspaces 84 Sturm bound 4423680

## Defining parameters

 Level: $$N$$ = $$6080 = 2^{6} \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$4423680$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6080))$$.

Total New Old
Modular forms 1116288 569316 546972
Cusp forms 1095553 564828 530725
Eisenstein series 20735 4488 16247

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6080))$$

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
6080.2.a $$\chi_{6080}(1, \cdot)$$ 6080.2.a.a 1 1
6080.2.a.b 1
6080.2.a.c 1
6080.2.a.d 1
6080.2.a.e 1
6080.2.a.f 1
6080.2.a.g 1
6080.2.a.h 1
6080.2.a.i 1
6080.2.a.j 1
6080.2.a.k 1
6080.2.a.l 1
6080.2.a.m 1
6080.2.a.n 1
6080.2.a.o 1
6080.2.a.p 1
6080.2.a.q 1
6080.2.a.r 1
6080.2.a.s 1
6080.2.a.t 1
6080.2.a.u 1
6080.2.a.v 1
6080.2.a.w 1
6080.2.a.x 1
6080.2.a.y 2
6080.2.a.z 2
6080.2.a.ba 2
6080.2.a.bb 2
6080.2.a.bc 2
6080.2.a.bd 2
6080.2.a.be 2
6080.2.a.bf 2
6080.2.a.bg 2
6080.2.a.bh 2
6080.2.a.bi 2
6080.2.a.bj 2
6080.2.a.bk 2
6080.2.a.bl 2
6080.2.a.bm 3
6080.2.a.bn 3
6080.2.a.bo 3
6080.2.a.bp 3
6080.2.a.bq 3
6080.2.a.br 3
6080.2.a.bs 3
6080.2.a.bt 3
6080.2.a.bu 3
6080.2.a.bv 3
6080.2.a.bw 3
6080.2.a.bx 3
6080.2.a.by 3
6080.2.a.bz 3
6080.2.a.ca 3
6080.2.a.cb 3
6080.2.a.cc 4
6080.2.a.cd 4
6080.2.a.ce 4
6080.2.a.cf 4
6080.2.a.cg 4
6080.2.a.ch 4
6080.2.a.ci 5
6080.2.a.cj 5
6080.2.a.ck 5
6080.2.a.cl 5
6080.2.d $$\chi_{6080}(3649, \cdot)$$ n/a 216 1
6080.2.e $$\chi_{6080}(5471, \cdot)$$ n/a 160 1
6080.2.f $$\chi_{6080}(3041, \cdot)$$ n/a 144 1
6080.2.g $$\chi_{6080}(6079, \cdot)$$ n/a 236 1
6080.2.j $$\chi_{6080}(2431, \cdot)$$ n/a 160 1
6080.2.k $$\chi_{6080}(609, \cdot)$$ n/a 216 1
6080.2.p $$\chi_{6080}(3039, \cdot)$$ n/a 240 1
6080.2.q $$\chi_{6080}(961, \cdot)$$ n/a 320 2
6080.2.r $$\chi_{6080}(113, \cdot)$$ n/a 472 2
6080.2.t $$\chi_{6080}(1103, \cdot)$$ n/a 432 2
6080.2.w $$\chi_{6080}(1519, \cdot)$$ n/a 472 2
6080.2.y $$\chi_{6080}(1521, \cdot)$$ n/a 288 2
6080.2.bb $$\chi_{6080}(417, \cdot)$$ n/a 480 2
6080.2.bc $$\chi_{6080}(1407, \cdot)$$ n/a 432 2
6080.2.bd $$\chi_{6080}(3457, \cdot)$$ n/a 472 2
6080.2.be $$\chi_{6080}(4447, \cdot)$$ n/a 432 2
6080.2.bi $$\chi_{6080}(2129, \cdot)$$ n/a 432 2
6080.2.bk $$\chi_{6080}(911, \cdot)$$ n/a 320 2
6080.2.bl $$\chi_{6080}(4143, \cdot)$$ n/a 432 2
6080.2.bn $$\chi_{6080}(3153, \cdot)$$ n/a 472 2
6080.2.bp $$\chi_{6080}(1569, \cdot)$$ n/a 480 2
6080.2.bq $$\chi_{6080}(1471, \cdot)$$ n/a 320 2
6080.2.bv $$\chi_{6080}(2079, \cdot)$$ n/a 480 2
6080.2.by $$\chi_{6080}(31, \cdot)$$ n/a 320 2
6080.2.bz $$\chi_{6080}(3009, \cdot)$$ n/a 472 2
6080.2.ca $$\chi_{6080}(639, \cdot)$$ n/a 472 2
6080.2.cb $$\chi_{6080}(2401, \cdot)$$ n/a 320 2
6080.2.ce $$\chi_{6080}(873, \cdot)$$ None 0 4
6080.2.cf $$\chi_{6080}(1863, \cdot)$$ None 0 4
6080.2.ck $$\chi_{6080}(151, \cdot)$$ None 0 4
6080.2.cl $$\chi_{6080}(761, \cdot)$$ None 0 4
6080.2.co $$\chi_{6080}(1369, \cdot)$$ None 0 4
6080.2.cp $$\chi_{6080}(759, \cdot)$$ None 0 4
6080.2.cq $$\chi_{6080}(343, \cdot)$$ None 0 4
6080.2.cr $$\chi_{6080}(2393, \cdot)$$ None 0 4
6080.2.cu $$\chi_{6080}(321, \cdot)$$ n/a 960 6
6080.2.cv $$\chi_{6080}(2193, \cdot)$$ n/a 944 4
6080.2.cx $$\chi_{6080}(847, \cdot)$$ n/a 944 4
6080.2.da $$\chi_{6080}(881, \cdot)$$ n/a 640 4
6080.2.dc $$\chi_{6080}(559, \cdot)$$ n/a 944 4
6080.2.dd $$\chi_{6080}(673, \cdot)$$ n/a 960 4
6080.2.de $$\chi_{6080}(767, \cdot)$$ n/a 944 4
6080.2.dj $$\chi_{6080}(2497, \cdot)$$ n/a 944 4
6080.2.dk $$\chi_{6080}(543, \cdot)$$ n/a 960 4
6080.2.dm $$\chi_{6080}(1551, \cdot)$$ n/a 640 4
6080.2.do $$\chi_{6080}(49, \cdot)$$ n/a 944 4
6080.2.dp $$\chi_{6080}(463, \cdot)$$ n/a 944 4
6080.2.dr $$\chi_{6080}(753, \cdot)$$ n/a 944 4
6080.2.dv $$\chi_{6080}(797, \cdot)$$ n/a 7648 8
6080.2.dw $$\chi_{6080}(1027, \cdot)$$ n/a 6912 8
6080.2.dx $$\chi_{6080}(379, \cdot)$$ n/a 7648 8
6080.2.dy $$\chi_{6080}(381, \cdot)$$ n/a 4608 8
6080.2.dz $$\chi_{6080}(229, \cdot)$$ n/a 6912 8
6080.2.ea $$\chi_{6080}(531, \cdot)$$ n/a 5120 8
6080.2.eh $$\chi_{6080}(267, \cdot)$$ n/a 6912 8
6080.2.ei $$\chi_{6080}(37, \cdot)$$ n/a 7648 8
6080.2.ej $$\chi_{6080}(1439, \cdot)$$ n/a 1440 6
6080.2.eo $$\chi_{6080}(161, \cdot)$$ n/a 960 6
6080.2.ep $$\chi_{6080}(319, \cdot)$$ n/a 1416 6
6080.2.es $$\chi_{6080}(769, \cdot)$$ n/a 1416 6
6080.2.et $$\chi_{6080}(991, \cdot)$$ n/a 960 6
6080.2.eu $$\chi_{6080}(831, \cdot)$$ n/a 960 6
6080.2.ev $$\chi_{6080}(289, \cdot)$$ n/a 1440 6
6080.2.ey $$\chi_{6080}(87, \cdot)$$ None 0 8
6080.2.ez $$\chi_{6080}(217, \cdot)$$ None 0 8
6080.2.fe $$\chi_{6080}(1319, \cdot)$$ None 0 8
6080.2.ff $$\chi_{6080}(729, \cdot)$$ None 0 8
6080.2.fi $$\chi_{6080}(121, \cdot)$$ None 0 8
6080.2.fj $$\chi_{6080}(711, \cdot)$$ None 0 8
6080.2.fk $$\chi_{6080}(297, \cdot)$$ None 0 8
6080.2.fl $$\chi_{6080}(7, \cdot)$$ None 0 8
6080.2.fo $$\chi_{6080}(529, \cdot)$$ n/a 2832 12
6080.2.fp $$\chi_{6080}(431, \cdot)$$ n/a 1920 12
6080.2.fu $$\chi_{6080}(193, \cdot)$$ n/a 2832 12
6080.2.fv $$\chi_{6080}(1183, \cdot)$$ n/a 2880 12
6080.2.fy $$\chi_{6080}(207, \cdot)$$ n/a 2832 12
6080.2.fz $$\chi_{6080}(497, \cdot)$$ n/a 2832 12
6080.2.gc $$\chi_{6080}(337, \cdot)$$ n/a 2832 12
6080.2.gd $$\chi_{6080}(47, \cdot)$$ n/a 2832 12
6080.2.gg $$\chi_{6080}(33, \cdot)$$ n/a 2880 12
6080.2.gh $$\chi_{6080}(63, \cdot)$$ n/a 2832 12
6080.2.gi $$\chi_{6080}(81, \cdot)$$ n/a 1920 12
6080.2.gj $$\chi_{6080}(79, \cdot)$$ n/a 2832 12
6080.2.go $$\chi_{6080}(597, \cdot)$$ n/a 15296 16
6080.2.gp $$\chi_{6080}(83, \cdot)$$ n/a 15296 16
6080.2.gq $$\chi_{6080}(331, \cdot)$$ n/a 10240 16
6080.2.gr $$\chi_{6080}(349, \cdot)$$ n/a 15296 16
6080.2.gs $$\chi_{6080}(501, \cdot)$$ n/a 10240 16
6080.2.gt $$\chi_{6080}(179, \cdot)$$ n/a 15296 16
6080.2.ha $$\chi_{6080}(387, \cdot)$$ n/a 15296 16
6080.2.hb $$\chi_{6080}(293, \cdot)$$ n/a 15296 16
6080.2.he $$\chi_{6080}(793, \cdot)$$ None 0 24
6080.2.hf $$\chi_{6080}(23, \cdot)$$ None 0 24
6080.2.hg $$\chi_{6080}(441, \cdot)$$ None 0 24
6080.2.hh $$\chi_{6080}(279, \cdot)$$ None 0 24
6080.2.hi $$\chi_{6080}(9, \cdot)$$ None 0 24
6080.2.hj $$\chi_{6080}(71, \cdot)$$ None 0 24
6080.2.hq $$\chi_{6080}(263, \cdot)$$ None 0 24
6080.2.hr $$\chi_{6080}(393, \cdot)$$ None 0 24
6080.2.hs $$\chi_{6080}(13, \cdot)$$ n/a 45888 48
6080.2.ht $$\chi_{6080}(43, \cdot)$$ n/a 45888 48
6080.2.hy $$\chi_{6080}(53, \cdot)$$ n/a 45888 48
6080.2.hz $$\chi_{6080}(187, \cdot)$$ n/a 45888 48
6080.2.ic $$\chi_{6080}(59, \cdot)$$ n/a 45888 48
6080.2.id $$\chi_{6080}(51, \cdot)$$ n/a 30720 48
6080.2.ie $$\chi_{6080}(149, \cdot)$$ n/a 45888 48
6080.2.if $$\chi_{6080}(61, \cdot)$$ n/a 30720 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6080))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6080)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(608))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1216))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1520))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3040))$$$$^{\oplus 2}$$