# Properties

 Label 8640.2 Level 8640 Weight 2 Dimension 808896 Nonzero newspaces 84 Sturm bound 7962624

## Defining parameters

 Level: $$N$$ = $$8640 = 2^{6} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$7962624$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8640))$$.

Total New Old
Modular forms 2007936 813120 1194816
Cusp forms 1973377 808896 1164481
Eisenstein series 34559 4224 30335

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8640))$$

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
8640.2.a $$\chi_{8640}(1, \cdot)$$ 8640.2.a.a 1 1
8640.2.a.b 1
8640.2.a.c 1
8640.2.a.d 1
8640.2.a.e 1
8640.2.a.f 1
8640.2.a.g 1
8640.2.a.h 1
8640.2.a.i 1
8640.2.a.j 1
8640.2.a.k 1
8640.2.a.l 1
8640.2.a.m 1
8640.2.a.n 1
8640.2.a.o 1
8640.2.a.p 1
8640.2.a.q 1
8640.2.a.r 1
8640.2.a.s 1
8640.2.a.t 1
8640.2.a.u 1
8640.2.a.v 1
8640.2.a.w 1
8640.2.a.x 1
8640.2.a.y 1
8640.2.a.z 1
8640.2.a.ba 1
8640.2.a.bb 1
8640.2.a.bc 1
8640.2.a.bd 1
8640.2.a.be 1
8640.2.a.bf 1
8640.2.a.bg 1
8640.2.a.bh 1
8640.2.a.bi 1
8640.2.a.bj 1
8640.2.a.bk 1
8640.2.a.bl 1
8640.2.a.bm 1
8640.2.a.bn 1
8640.2.a.bo 1
8640.2.a.bp 1
8640.2.a.bq 1
8640.2.a.br 1
8640.2.a.bs 1
8640.2.a.bt 1
8640.2.a.bu 1
8640.2.a.bv 1
8640.2.a.bw 1
8640.2.a.bx 1
8640.2.a.by 1
8640.2.a.bz 1
8640.2.a.ca 1
8640.2.a.cb 1
8640.2.a.cc 1
8640.2.a.cd 1
8640.2.a.ce 1
8640.2.a.cf 1
8640.2.a.cg 1
8640.2.a.ch 1
8640.2.a.ci 2
8640.2.a.cj 2
8640.2.a.ck 2
8640.2.a.cl 2
8640.2.a.cm 2
8640.2.a.cn 2
8640.2.a.co 2
8640.2.a.cp 2
8640.2.a.cq 2
8640.2.a.cr 2
8640.2.a.cs 2
8640.2.a.ct 2
8640.2.a.cu 2
8640.2.a.cv 2
8640.2.a.cw 2
8640.2.a.cx 2
8640.2.a.cy 2
8640.2.a.cz 2
8640.2.a.da 2
8640.2.a.db 2
8640.2.a.dc 2
8640.2.a.dd 2
8640.2.a.de 2
8640.2.a.df 2
8640.2.a.dg 2
8640.2.a.dh 2
8640.2.a.di 2
8640.2.a.dj 2
8640.2.a.dk 3
8640.2.a.dl 3
8640.2.a.dm 3
8640.2.a.dn 3
8640.2.b $$\chi_{8640}(2591, \cdot)$$ n/a 128 1
8640.2.d $$\chi_{8640}(6049, \cdot)$$ n/a 192 1
8640.2.f $$\chi_{8640}(1729, \cdot)$$ n/a 192 1
8640.2.h $$\chi_{8640}(6911, \cdot)$$ n/a 128 1
8640.2.k $$\chi_{8640}(4321, \cdot)$$ n/a 128 1
8640.2.m $$\chi_{8640}(4319, \cdot)$$ n/a 192 1
8640.2.o $$\chi_{8640}(8639, \cdot)$$ n/a 192 1
8640.2.q $$\chi_{8640}(2881, \cdot)$$ n/a 192 2
8640.2.t $$\chi_{8640}(2161, \cdot)$$ n/a 256 2
8640.2.u $$\chi_{8640}(2159, \cdot)$$ n/a 384 2
8640.2.w $$\chi_{8640}(2753, \cdot)$$ n/a 384 2
8640.2.x $$\chi_{8640}(703, \cdot)$$ n/a 384 2
8640.2.z $$\chi_{8640}(2863, \cdot)$$ n/a 384 2
8640.2.bc $$\chi_{8640}(593, \cdot)$$ n/a 384 2
8640.2.bd $$\chi_{8640}(7183, \cdot)$$ n/a 384 2
8640.2.bg $$\chi_{8640}(4913, \cdot)$$ n/a 384 2
8640.2.bi $$\chi_{8640}(1567, \cdot)$$ n/a 384 2
8640.2.bj $$\chi_{8640}(3617, \cdot)$$ n/a 384 2
8640.2.bl $$\chi_{8640}(431, \cdot)$$ n/a 256 2
8640.2.bm $$\chi_{8640}(3889, \cdot)$$ n/a 384 2
8640.2.br $$\chi_{8640}(2879, \cdot)$$ n/a 280 2
8640.2.bt $$\chi_{8640}(1439, \cdot)$$ n/a 288 2
8640.2.bv $$\chi_{8640}(1441, \cdot)$$ n/a 192 2
8640.2.bw $$\chi_{8640}(1151, \cdot)$$ n/a 192 2
8640.2.by $$\chi_{8640}(4609, \cdot)$$ n/a 280 2
8640.2.ca $$\chi_{8640}(289, \cdot)$$ n/a 288 2
8640.2.cc $$\chi_{8640}(5471, \cdot)$$ n/a 192 2
8640.2.ce $$\chi_{8640}(2647, \cdot)$$ None 0 4
8640.2.ch $$\chi_{8640}(377, \cdot)$$ None 0 4
8640.2.ci $$\chi_{8640}(1079, \cdot)$$ None 0 4
8640.2.cl $$\chi_{8640}(1081, \cdot)$$ None 0 4
8640.2.cn $$\chi_{8640}(1511, \cdot)$$ None 0 4
8640.2.co $$\chi_{8640}(649, \cdot)$$ None 0 4
8640.2.cr $$\chi_{8640}(2537, \cdot)$$ None 0 4
8640.2.cs $$\chi_{8640}(487, \cdot)$$ None 0 4
8640.2.cu $$\chi_{8640}(961, \cdot)$$ n/a 1728 6
8640.2.cv $$\chi_{8640}(1009, \cdot)$$ n/a 560 4
8640.2.cw $$\chi_{8640}(1871, \cdot)$$ n/a 384 4
8640.2.cz $$\chi_{8640}(2143, \cdot)$$ n/a 576 4
8640.2.dc $$\chi_{8640}(737, \cdot)$$ n/a 576 4
8640.2.dd $$\chi_{8640}(17, \cdot)$$ n/a 560 4
8640.2.dg $$\chi_{8640}(1423, \cdot)$$ n/a 560 4
8640.2.dh $$\chi_{8640}(3473, \cdot)$$ n/a 560 4
8640.2.dk $$\chi_{8640}(847, \cdot)$$ n/a 560 4
8640.2.dl $$\chi_{8640}(2177, \cdot)$$ n/a 560 4
8640.2.do $$\chi_{8640}(127, \cdot)$$ n/a 560 4
8640.2.dr $$\chi_{8640}(719, \cdot)$$ n/a 560 4
8640.2.ds $$\chi_{8640}(721, \cdot)$$ n/a 384 4
8640.2.du $$\chi_{8640}(917, \cdot)$$ n/a 6144 8
8640.2.dv $$\chi_{8640}(1027, \cdot)$$ n/a 6144 8
8640.2.dx $$\chi_{8640}(541, \cdot)$$ n/a 4096 8
8640.2.dz $$\chi_{8640}(109, \cdot)$$ n/a 6144 8
8640.2.ec $$\chi_{8640}(971, \cdot)$$ n/a 4096 8
8640.2.ee $$\chi_{8640}(539, \cdot)$$ n/a 6144 8
8640.2.eg $$\chi_{8640}(53, \cdot)$$ n/a 6144 8
8640.2.eh $$\chi_{8640}(163, \cdot)$$ n/a 6144 8
8640.2.ej $$\chi_{8640}(479, \cdot)$$ n/a 2592 6
8640.2.eo $$\chi_{8640}(481, \cdot)$$ n/a 1728 6
8640.2.ep $$\chi_{8640}(959, \cdot)$$ n/a 2568 6
8640.2.es $$\chi_{8640}(769, \cdot)$$ n/a 2568 6
8640.2.et $$\chi_{8640}(671, \cdot)$$ n/a 1728 6
8640.2.eu $$\chi_{8640}(191, \cdot)$$ n/a 1728 6
8640.2.ev $$\chi_{8640}(1249, \cdot)$$ n/a 2592 6
8640.2.ez $$\chi_{8640}(343, \cdot)$$ None 0 8
8640.2.fa $$\chi_{8640}(953, \cdot)$$ None 0 8
8640.2.fc $$\chi_{8640}(361, \cdot)$$ None 0 8
8640.2.ff $$\chi_{8640}(359, \cdot)$$ None 0 8
8640.2.fh $$\chi_{8640}(1369, \cdot)$$ None 0 8
8640.2.fi $$\chi_{8640}(71, \cdot)$$ None 0 8
8640.2.fk $$\chi_{8640}(233, \cdot)$$ None 0 8
8640.2.fn $$\chi_{8640}(1063, \cdot)$$ None 0 8
8640.2.fq $$\chi_{8640}(239, \cdot)$$ n/a 5136 12
8640.2.fr $$\chi_{8640}(241, \cdot)$$ n/a 3456 12
8640.2.fu $$\chi_{8640}(353, \cdot)$$ n/a 5184 12
8640.2.fv $$\chi_{8640}(1087, \cdot)$$ n/a 5136 12
8640.2.fw $$\chi_{8640}(367, \cdot)$$ n/a 5136 12
8640.2.fy $$\chi_{8640}(113, \cdot)$$ n/a 5136 12
8640.2.ga $$\chi_{8640}(497, \cdot)$$ n/a 5136 12
8640.2.gc $$\chi_{8640}(943, \cdot)$$ n/a 5136 12
8640.2.gg $$\chi_{8640}(257, \cdot)$$ n/a 5136 12
8640.2.gh $$\chi_{8640}(223, \cdot)$$ n/a 5184 12
8640.2.gk $$\chi_{8640}(49, \cdot)$$ n/a 5136 12
8640.2.gl $$\chi_{8640}(911, \cdot)$$ n/a 3456 12
8640.2.gm $$\chi_{8640}(307, \cdot)$$ n/a 9152 16
8640.2.gp $$\chi_{8640}(197, \cdot)$$ n/a 9152 16
8640.2.gr $$\chi_{8640}(179, \cdot)$$ n/a 9152 16
8640.2.gt $$\chi_{8640}(251, \cdot)$$ n/a 6144 16
8640.2.gu $$\chi_{8640}(469, \cdot)$$ n/a 9152 16
8640.2.gw $$\chi_{8640}(181, \cdot)$$ n/a 6144 16
8640.2.gy $$\chi_{8640}(667, \cdot)$$ n/a 9152 16
8640.2.hb $$\chi_{8640}(557, \cdot)$$ n/a 9152 16
8640.2.he $$\chi_{8640}(169, \cdot)$$ None 0 24
8640.2.hf $$\chi_{8640}(311, \cdot)$$ None 0 24
8640.2.hg $$\chi_{8640}(137, \cdot)$$ None 0 24
8640.2.hj $$\chi_{8640}(103, \cdot)$$ None 0 24
8640.2.hk $$\chi_{8640}(713, \cdot)$$ None 0 24
8640.2.hn $$\chi_{8640}(7, \cdot)$$ None 0 24
8640.2.ho $$\chi_{8640}(119, \cdot)$$ None 0 24
8640.2.hp $$\chi_{8640}(121, \cdot)$$ None 0 24
8640.2.ht $$\chi_{8640}(77, \cdot)$$ n/a 82752 48
8640.2.hu $$\chi_{8640}(187, \cdot)$$ n/a 82752 48
8640.2.hw $$\chi_{8640}(61, \cdot)$$ n/a 55296 48
8640.2.hz $$\chi_{8640}(59, \cdot)$$ n/a 82752 48
8640.2.ib $$\chi_{8640}(229, \cdot)$$ n/a 82752 48
8640.2.ic $$\chi_{8640}(11, \cdot)$$ n/a 55296 48
8640.2.ie $$\chi_{8640}(43, \cdot)$$ n/a 82752 48
8640.2.ih $$\chi_{8640}(173, \cdot)$$ n/a 82752 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8640))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8640)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 56}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 48}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 42}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 21}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(432))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(480))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(576))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(720))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(864))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(960))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1080))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1440))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1728))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2160))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2880))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4320))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8640))$$$$^{\oplus 1}$$