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Properties

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

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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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(6480)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 50}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 25}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(810))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1080))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1620))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3240))\)\(^{\oplus 2}\)