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Properties

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

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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

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