# Properties

 Label 9280.2 Level 9280 Weight 2 Dimension 1323828 Nonzero newspaces 104 Sturm bound 10321920

## Defining parameters

 Level: $$N$$ = $$9280 = 2^{6} \cdot 5 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$104$$ Sturm bound: $$10321920$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9280))$$.

Total New Old
Modular forms 2596608 1330956 1265652
Cusp forms 2564353 1323828 1240525
Eisenstein series 32255 7128 25127

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9280))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
9280.2.a $$\chi_{9280}(1, \cdot)$$ 9280.2.a.a 1 1
9280.2.a.b 1
9280.2.a.c 1
9280.2.a.d 1
9280.2.a.e 1
9280.2.a.f 1
9280.2.a.g 1
9280.2.a.h 1
9280.2.a.i 1
9280.2.a.j 1
9280.2.a.k 1
9280.2.a.l 1
9280.2.a.m 1
9280.2.a.n 1
9280.2.a.o 1
9280.2.a.p 1
9280.2.a.q 1
9280.2.a.r 1
9280.2.a.s 1
9280.2.a.t 1
9280.2.a.u 1
9280.2.a.v 1
9280.2.a.w 2
9280.2.a.x 2
9280.2.a.y 2
9280.2.a.z 2
9280.2.a.ba 2
9280.2.a.bb 2
9280.2.a.bc 2
9280.2.a.bd 2
9280.2.a.be 2
9280.2.a.bf 3
9280.2.a.bg 3
9280.2.a.bh 3
9280.2.a.bi 3
9280.2.a.bj 3
9280.2.a.bk 3
9280.2.a.bl 3
9280.2.a.bm 3
9280.2.a.bn 3
9280.2.a.bo 3
9280.2.a.bp 3
9280.2.a.bq 3
9280.2.a.br 3
9280.2.a.bs 3
9280.2.a.bt 3
9280.2.a.bu 3
9280.2.a.bv 3
9280.2.a.bw 3
9280.2.a.bx 3
9280.2.a.by 3
9280.2.a.bz 4
9280.2.a.ca 4
9280.2.a.cb 4
9280.2.a.cc 4
9280.2.a.cd 4
9280.2.a.ce 4
9280.2.a.cf 4
9280.2.a.cg 5
9280.2.a.ch 5
9280.2.a.ci 5
9280.2.a.cj 5
9280.2.a.ck 5
9280.2.a.cl 5
9280.2.a.cm 6
9280.2.a.cn 6
9280.2.a.co 6
9280.2.a.cp 6
9280.2.a.cq 7
9280.2.a.cr 7
9280.2.a.cs 8
9280.2.a.ct 10
9280.2.a.cu 10
9280.2.d $$\chi_{9280}(5569, \cdot)$$ n/a 336 1
9280.2.e $$\chi_{9280}(289, \cdot)$$ n/a 360 1
9280.2.f $$\chi_{9280}(4641, \cdot)$$ n/a 224 1
9280.2.g $$\chi_{9280}(8641, \cdot)$$ n/a 240 1
9280.2.j $$\chi_{9280}(4929, \cdot)$$ n/a 356 1
9280.2.k $$\chi_{9280}(929, \cdot)$$ n/a 336 1
9280.2.p $$\chi_{9280}(4001, \cdot)$$ n/a 240 1
9280.2.q $$\chi_{9280}(1839, \cdot)$$ n/a 712 2
9280.2.t $$\chi_{9280}(5103, \cdot)$$ n/a 712 2
9280.2.u $$\chi_{9280}(737, \cdot)$$ n/a 720 2
9280.2.w $$\chi_{9280}(6977, \cdot)$$ n/a 712 2
9280.2.z $$\chi_{9280}(1103, \cdot)$$ n/a 672 2
9280.2.bb $$\chi_{9280}(911, \cdot)$$ n/a 480 2
9280.2.bc $$\chi_{9280}(191, \cdot)$$ n/a 480 2
9280.2.bf $$\chi_{9280}(1681, \cdot)$$ n/a 480 2
9280.2.bh $$\chi_{9280}(2321, \cdot)$$ n/a 448 2
9280.2.bi $$\chi_{9280}(3231, \cdot)$$ n/a 480 2
9280.2.bl $$\chi_{9280}(17, \cdot)$$ n/a 712 2
9280.2.bo $$\chi_{9280}(6207, \cdot)$$ n/a 672 2
9280.2.bp $$\chi_{9280}(927, \cdot)$$ n/a 720 2
9280.2.bq $$\chi_{9280}(1873, \cdot)$$ n/a 712 2
9280.2.bs $$\chi_{9280}(6513, \cdot)$$ n/a 712 2
9280.2.bu $$\chi_{9280}(1567, \cdot)$$ n/a 672 2
9280.2.bv $$\chi_{9280}(5567, \cdot)$$ n/a 712 2
9280.2.bz $$\chi_{9280}(273, \cdot)$$ n/a 712 2
9280.2.cb $$\chi_{9280}(1119, \cdot)$$ n/a 720 2
9280.2.cc $$\chi_{9280}(3249, \cdot)$$ n/a 672 2
9280.2.ce $$\chi_{9280}(2609, \cdot)$$ n/a 712 2
9280.2.ch $$\chi_{9280}(4159, \cdot)$$ n/a 712 2
9280.2.cj $$\chi_{9280}(3439, \cdot)$$ n/a 712 2
9280.2.ck $$\chi_{9280}(5743, \cdot)$$ n/a 672 2
9280.2.cn $$\chi_{9280}(5377, \cdot)$$ n/a 712 2
9280.2.cp $$\chi_{9280}(2337, \cdot)$$ n/a 720 2
9280.2.cq $$\chi_{9280}(463, \cdot)$$ n/a 712 2
9280.2.cs $$\chi_{9280}(2511, \cdot)$$ n/a 480 2
9280.2.cu $$\chi_{9280}(1921, \cdot)$$ n/a 1440 6
9280.2.cw $$\chi_{9280}(1177, \cdot)$$ None 0 4
9280.2.cy $$\chi_{9280}(407, \cdot)$$ None 0 4
9280.2.da $$\chi_{9280}(3943, \cdot)$$ None 0 4
9280.2.db $$\chi_{9280}(713, \cdot)$$ None 0 4
9280.2.dd $$\chi_{9280}(1449, \cdot)$$ None 0 4
9280.2.dg $$\chi_{9280}(1161, \cdot)$$ None 0 4
9280.2.dh $$\chi_{9280}(3671, \cdot)$$ None 0 4
9280.2.dk $$\chi_{9280}(1351, \cdot)$$ None 0 4
9280.2.dl $$\chi_{9280}(679, \cdot)$$ None 0 4
9280.2.do $$\chi_{9280}(2279, \cdot)$$ None 0 4
9280.2.dq $$\chi_{9280}(521, \cdot)$$ None 0 4
9280.2.dr $$\chi_{9280}(2089, \cdot)$$ None 0 4
9280.2.dt $$\chi_{9280}(1433, \cdot)$$ None 0 4
9280.2.dv $$\chi_{9280}(2263, \cdot)$$ None 0 4
9280.2.dx $$\chi_{9280}(1623, \cdot)$$ None 0 4
9280.2.ea $$\chi_{9280}(1897, \cdot)$$ None 0 4
9280.2.eb $$\chi_{9280}(2081, \cdot)$$ n/a 1440 6
9280.2.eg $$\chi_{9280}(2849, \cdot)$$ n/a 2160 6
9280.2.eh $$\chi_{9280}(129, \cdot)$$ n/a 2136 6
9280.2.ek $$\chi_{9280}(961, \cdot)$$ n/a 1440 6
9280.2.el $$\chi_{9280}(161, \cdot)$$ n/a 1440 6
9280.2.em $$\chi_{9280}(1889, \cdot)$$ n/a 2160 6
9280.2.en $$\chi_{9280}(1089, \cdot)$$ n/a 2136 6
9280.2.er $$\chi_{9280}(347, \cdot)$$ n/a 11488 8
9280.2.es $$\chi_{9280}(1259, \cdot)$$ n/a 11488 8
9280.2.eu $$\chi_{9280}(1491, \cdot)$$ n/a 7680 8
9280.2.ex $$\chi_{9280}(523, \cdot)$$ n/a 10752 8
9280.2.ez $$\chi_{9280}(581, \cdot)$$ n/a 7168 8
9280.2.fa $$\chi_{9280}(349, \cdot)$$ n/a 10752 8
9280.2.fc $$\chi_{9280}(133, \cdot)$$ n/a 11488 8
9280.2.ff $$\chi_{9280}(597, \cdot)$$ n/a 11488 8
9280.2.fg $$\chi_{9280}(1293, \cdot)$$ n/a 11488 8
9280.2.fj $$\chi_{9280}(853, \cdot)$$ n/a 11488 8
9280.2.fl $$\chi_{9280}(1101, \cdot)$$ n/a 7680 8
9280.2.fm $$\chi_{9280}(869, \cdot)$$ n/a 11488 8
9280.2.fo $$\chi_{9280}(1507, \cdot)$$ n/a 11488 8
9280.2.fr $$\chi_{9280}(99, \cdot)$$ n/a 11488 8
9280.2.ft $$\chi_{9280}(331, \cdot)$$ n/a 7680 8
9280.2.fu $$\chi_{9280}(987, \cdot)$$ n/a 10752 8
9280.2.fx $$\chi_{9280}(591, \cdot)$$ n/a 2880 12
9280.2.fz $$\chi_{9280}(1327, \cdot)$$ n/a 4272 12
9280.2.ga $$\chi_{9280}(193, \cdot)$$ n/a 4272 12
9280.2.gc $$\chi_{9280}(417, \cdot)$$ n/a 4320 12
9280.2.gf $$\chi_{9280}(1167, \cdot)$$ n/a 4272 12
9280.2.gg $$\chi_{9280}(1519, \cdot)$$ n/a 4272 12
9280.2.gi $$\chi_{9280}(959, \cdot)$$ n/a 4272 12
9280.2.gl $$\chi_{9280}(49, \cdot)$$ n/a 4272 12
9280.2.gn $$\chi_{9280}(209, \cdot)$$ n/a 4272 12
9280.2.go $$\chi_{9280}(159, \cdot)$$ n/a 4320 12
9280.2.gr $$\chi_{9280}(177, \cdot)$$ n/a 4272 12
9280.2.gu $$\chi_{9280}(63, \cdot)$$ n/a 4272 12
9280.2.gv $$\chi_{9280}(223, \cdot)$$ n/a 4320 12
9280.2.gw $$\chi_{9280}(337, \cdot)$$ n/a 4272 12
9280.2.gy $$\chi_{9280}(913, \cdot)$$ n/a 4272 12
9280.2.ha $$\chi_{9280}(863, \cdot)$$ n/a 4320 12
9280.2.hb $$\chi_{9280}(703, \cdot)$$ n/a 4272 12
9280.2.hf $$\chi_{9280}(113, \cdot)$$ n/a 4272 12
9280.2.hh $$\chi_{9280}(31, \cdot)$$ n/a 2880 12
9280.2.hi $$\chi_{9280}(241, \cdot)$$ n/a 2880 12
9280.2.hk $$\chi_{9280}(81, \cdot)$$ n/a 2880 12
9280.2.hn $$\chi_{9280}(511, \cdot)$$ n/a 2880 12
9280.2.ho $$\chi_{9280}(271, \cdot)$$ n/a 2880 12
9280.2.hq $$\chi_{9280}(687, \cdot)$$ n/a 4272 12
9280.2.ht $$\chi_{9280}(97, \cdot)$$ n/a 4320 12
9280.2.hv $$\chi_{9280}(2177, \cdot)$$ n/a 4272 12
9280.2.hw $$\chi_{9280}(207, \cdot)$$ n/a 4272 12
9280.2.hz $$\chi_{9280}(79, \cdot)$$ n/a 4272 12
9280.2.ia $$\chi_{9280}(137, \cdot)$$ None 0 24
9280.2.ic $$\chi_{9280}(167, \cdot)$$ None 0 24
9280.2.ie $$\chi_{9280}(7, \cdot)$$ None 0 24
9280.2.ih $$\chi_{9280}(617, \cdot)$$ None 0 24
9280.2.ii $$\chi_{9280}(281, \cdot)$$ None 0 24
9280.2.il $$\chi_{9280}(9, \cdot)$$ None 0 24
9280.2.in $$\chi_{9280}(279, \cdot)$$ None 0 24
9280.2.io $$\chi_{9280}(39, \cdot)$$ None 0 24
9280.2.ir $$\chi_{9280}(391, \cdot)$$ None 0 24
9280.2.is $$\chi_{9280}(311, \cdot)$$ None 0 24
9280.2.iv $$\chi_{9280}(169, \cdot)$$ None 0 24
9280.2.iw $$\chi_{9280}(121, \cdot)$$ None 0 24
9280.2.iz $$\chi_{9280}(73, \cdot)$$ None 0 24
9280.2.jb $$\chi_{9280}(903, \cdot)$$ None 0 24
9280.2.jd $$\chi_{9280}(103, \cdot)$$ None 0 24
9280.2.je $$\chi_{9280}(537, \cdot)$$ None 0 24
9280.2.jg $$\chi_{9280}(123, \cdot)$$ n/a 68928 48
9280.2.jj $$\chi_{9280}(11, \cdot)$$ n/a 46080 48
9280.2.jl $$\chi_{9280}(19, \cdot)$$ n/a 68928 48
9280.2.jm $$\chi_{9280}(187, \cdot)$$ n/a 68928 48
9280.2.jp $$\chi_{9280}(109, \cdot)$$ n/a 68928 48
9280.2.jq $$\chi_{9280}(341, \cdot)$$ n/a 46080 48
9280.2.js $$\chi_{9280}(77, \cdot)$$ n/a 68928 48
9280.2.jv $$\chi_{9280}(37, \cdot)$$ n/a 68928 48
9280.2.jw $$\chi_{9280}(437, \cdot)$$ n/a 68928 48
9280.2.jz $$\chi_{9280}(293, \cdot)$$ n/a 68928 48
9280.2.kb $$\chi_{9280}(429, \cdot)$$ n/a 68928 48
9280.2.kc $$\chi_{9280}(141, \cdot)$$ n/a 46080 48
9280.2.kf $$\chi_{9280}(83, \cdot)$$ n/a 68928 48
9280.2.kg $$\chi_{9280}(171, \cdot)$$ n/a 46080 48
9280.2.ki $$\chi_{9280}(259, \cdot)$$ n/a 68928 48
9280.2.kl $$\chi_{9280}(67, \cdot)$$ n/a 68928 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9280))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9280)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(232))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(290))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(464))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(580))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(928))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1856))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2320))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4640))$$$$^{\oplus 2}$$