↑

Properties

Label 8280.2
Level 8280
Weight 2
Dimension 739786
Nonzero newspaces 72
Sturm bound 7299072

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(7299072\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8280))\).

Total New Old
Modular forms 1841664 744322 1097342
Cusp forms 1807873 739786 1068087
Eisenstein series 33791 4536 29255

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8280))\)

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
8280.2.a \(\chi_{8280}(1, \cdot)\) 8280.2.a.a 1 1
8280.2.a.b 1
8280.2.a.c 1
8280.2.a.d 1
8280.2.a.e 1
8280.2.a.f 1
8280.2.a.g 1
8280.2.a.h 1
8280.2.a.i 1
8280.2.a.j 1
8280.2.a.k 1
8280.2.a.l 1
8280.2.a.m 1
8280.2.a.n 1
8280.2.a.o 1
8280.2.a.p 1
8280.2.a.q 1
8280.2.a.r 1
8280.2.a.s 1
8280.2.a.t 1
8280.2.a.u 1
8280.2.a.v 1
8280.2.a.w 1
8280.2.a.x 2
8280.2.a.y 2
8280.2.a.z 2
8280.2.a.ba 2
8280.2.a.bb 2
8280.2.a.bc 2
8280.2.a.bd 2
8280.2.a.be 2
8280.2.a.bf 2
8280.2.a.bg 2
8280.2.a.bh 3
8280.2.a.bi 3
8280.2.a.bj 3
8280.2.a.bk 3
8280.2.a.bl 3
8280.2.a.bm 3
8280.2.a.bn 3
8280.2.a.bo 3
8280.2.a.bp 3
8280.2.a.bq 4
8280.2.a.br 5
8280.2.a.bs 5
8280.2.a.bt 6
8280.2.a.bu 6
8280.2.a.bv 7
8280.2.a.bw 7
8280.2.c \(\chi_{8280}(5291, \cdot)\) n/a 352 1
8280.2.e \(\chi_{8280}(5381, \cdot)\) n/a 384 1
8280.2.f \(\chi_{8280}(829, \cdot)\) n/a 660 1
8280.2.h \(\chi_{8280}(5059, \cdot)\) n/a 716 1
8280.2.k \(\chi_{8280}(4969, \cdot)\) n/a 164 1
8280.2.m \(\chi_{8280}(919, \cdot)\) None 0 1
8280.2.n \(\chi_{8280}(1151, \cdot)\) None 0 1
8280.2.p \(\chi_{8280}(1241, \cdot)\) 8280.2.p.a 48 1
8280.2.p.b 48
8280.2.r \(\chi_{8280}(91, \cdot)\) n/a 480 1
8280.2.t \(\chi_{8280}(4141, \cdot)\) n/a 440 1
8280.2.w \(\chi_{8280}(2069, \cdot)\) n/a 576 1
8280.2.y \(\chi_{8280}(1979, \cdot)\) n/a 528 1
8280.2.z \(\chi_{8280}(6209, \cdot)\) n/a 144 1
8280.2.bb \(\chi_{8280}(6119, \cdot)\) None 0 1
8280.2.be \(\chi_{8280}(4231, \cdot)\) None 0 1
8280.2.bg \(\chi_{8280}(2761, \cdot)\) n/a 528 2
8280.2.bj \(\chi_{8280}(4967, \cdot)\) None 0 2
8280.2.bk \(\chi_{8280}(737, \cdot)\) n/a 264 2
8280.2.bl \(\chi_{8280}(3727, \cdot)\) None 0 2
8280.2.bm \(\chi_{8280}(3817, \cdot)\) n/a 360 2
8280.2.br \(\chi_{8280}(1243, \cdot)\) n/a 1320 2
8280.2.bs \(\chi_{8280}(1333, \cdot)\) n/a 1432 2
8280.2.bt \(\chi_{8280}(827, \cdot)\) n/a 1152 2
8280.2.bu \(\chi_{8280}(4877, \cdot)\) n/a 1056 2
8280.2.bx \(\chi_{8280}(1471, \cdot)\) None 0 2
8280.2.cb \(\chi_{8280}(689, \cdot)\) n/a 864 2
8280.2.cd \(\chi_{8280}(599, \cdot)\) None 0 2
8280.2.ce \(\chi_{8280}(4829, \cdot)\) n/a 3440 2
8280.2.cg \(\chi_{8280}(4739, \cdot)\) n/a 3168 2
8280.2.cj \(\chi_{8280}(2851, \cdot)\) n/a 2304 2
8280.2.cl \(\chi_{8280}(1381, \cdot)\) n/a 2112 2
8280.2.cn \(\chi_{8280}(3911, \cdot)\) None 0 2
8280.2.cp \(\chi_{8280}(4001, \cdot)\) n/a 576 2
8280.2.cq \(\chi_{8280}(2209, \cdot)\) n/a 792 2
8280.2.cs \(\chi_{8280}(3679, \cdot)\) None 0 2
8280.2.cv \(\chi_{8280}(3589, \cdot)\) n/a 3168 2
8280.2.cx \(\chi_{8280}(2299, \cdot)\) n/a 3440 2
8280.2.cy \(\chi_{8280}(2531, \cdot)\) n/a 2112 2
8280.2.da \(\chi_{8280}(2621, \cdot)\) n/a 2304 2
8280.2.dc \(\chi_{8280}(361, \cdot)\) n/a 1200 10
8280.2.dd \(\chi_{8280}(2437, \cdot)\) n/a 6880 4
8280.2.de \(\chi_{8280}(2347, \cdot)\) n/a 6336 4
8280.2.dj \(\chi_{8280}(1013, \cdot)\) n/a 6336 4
8280.2.dk \(\chi_{8280}(3587, \cdot)\) n/a 6880 4
8280.2.dl \(\chi_{8280}(3497, \cdot)\) n/a 1584 4
8280.2.dm \(\chi_{8280}(1103, \cdot)\) None 0 4
8280.2.dr \(\chi_{8280}(1057, \cdot)\) n/a 1728 4
8280.2.ds \(\chi_{8280}(967, \cdot)\) None 0 4
8280.2.du \(\chi_{8280}(631, \cdot)\) None 0 10
8280.2.dx \(\chi_{8280}(719, \cdot)\) None 0 10
8280.2.dz \(\chi_{8280}(89, \cdot)\) n/a 1440 10
8280.2.ea \(\chi_{8280}(179, \cdot)\) n/a 5760 10
8280.2.ec \(\chi_{8280}(1349, \cdot)\) n/a 5760 10
8280.2.ef \(\chi_{8280}(541, \cdot)\) n/a 4800 10
8280.2.eh \(\chi_{8280}(451, \cdot)\) n/a 4800 10
8280.2.ej \(\chi_{8280}(521, \cdot)\) n/a 960 10
8280.2.el \(\chi_{8280}(71, \cdot)\) None 0 10
8280.2.em \(\chi_{8280}(199, \cdot)\) None 0 10
8280.2.eo \(\chi_{8280}(289, \cdot)\) n/a 1800 10
8280.2.er \(\chi_{8280}(19, \cdot)\) n/a 7160 10
8280.2.et \(\chi_{8280}(469, \cdot)\) n/a 7160 10
8280.2.eu \(\chi_{8280}(341, \cdot)\) n/a 3840 10
8280.2.ew \(\chi_{8280}(611, \cdot)\) n/a 3840 10
8280.2.ey \(\chi_{8280}(121, \cdot)\) n/a 5760 20
8280.2.fb \(\chi_{8280}(197, \cdot)\) n/a 11520 20
8280.2.fc \(\chi_{8280}(107, \cdot)\) n/a 11520 20
8280.2.fd \(\chi_{8280}(37, \cdot)\) n/a 14320 20
8280.2.fe \(\chi_{8280}(163, \cdot)\) n/a 14320 20
8280.2.fj \(\chi_{8280}(217, \cdot)\) n/a 3600 20
8280.2.fk \(\chi_{8280}(127, \cdot)\) None 0 20
8280.2.fl \(\chi_{8280}(233, \cdot)\) n/a 2880 20
8280.2.fm \(\chi_{8280}(143, \cdot)\) None 0 20
8280.2.fq \(\chi_{8280}(221, \cdot)\) n/a 23040 20
8280.2.fs \(\chi_{8280}(131, \cdot)\) n/a 23040 20
8280.2.ft \(\chi_{8280}(619, \cdot)\) n/a 34400 20
8280.2.fv \(\chi_{8280}(349, \cdot)\) n/a 34400 20
8280.2.fy \(\chi_{8280}(79, \cdot)\) None 0 20
8280.2.ga \(\chi_{8280}(49, \cdot)\) n/a 8640 20
8280.2.gb \(\chi_{8280}(281, \cdot)\) n/a 5760 20
8280.2.gd \(\chi_{8280}(311, \cdot)\) None 0 20
8280.2.gf \(\chi_{8280}(301, \cdot)\) n/a 23040 20
8280.2.gh \(\chi_{8280}(571, \cdot)\) n/a 23040 20
8280.2.gk \(\chi_{8280}(59, \cdot)\) n/a 34400 20
8280.2.gm \(\chi_{8280}(149, \cdot)\) n/a 34400 20
8280.2.gn \(\chi_{8280}(119, \cdot)\) None 0 20
8280.2.gp \(\chi_{8280}(329, \cdot)\) n/a 8640 20
8280.2.gt \(\chi_{8280}(511, \cdot)\) None 0 20
8280.2.gu \(\chi_{8280}(223, \cdot)\) None 0 40
8280.2.gv \(\chi_{8280}(97, \cdot)\) n/a 17280 40
8280.2.ha \(\chi_{8280}(263, \cdot)\) None 0 40
8280.2.hb \(\chi_{8280}(257, \cdot)\) n/a 17280 40
8280.2.hc \(\chi_{8280}(83, \cdot)\) n/a 68800 40
8280.2.hd \(\chi_{8280}(77, \cdot)\) n/a 68800 40
8280.2.hi \(\chi_{8280}(187, \cdot)\) n/a 68800 40
8280.2.hj \(\chi_{8280}(157, \cdot)\) n/a 68800 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2070))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4140))\)\(^{\oplus 2}\)