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Properties

Label 5580.2
Level 5580
Weight 2
Dimension 348826
Nonzero newspaces 120
Sturm bound 3317760

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Defining parameters

Level: \( N \) = \( 5580 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(3317760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5580))\).

Total New Old
Modular forms 839040 351954 487086
Cusp forms 819841 348826 471015
Eisenstein series 19199 3128 16071

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5580))\)

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
5580.2.a \(\chi_{5580}(1, \cdot)\) 5580.2.a.a 1 1
5580.2.a.b 1
5580.2.a.c 1
5580.2.a.d 1
5580.2.a.e 1
5580.2.a.f 1
5580.2.a.g 2
5580.2.a.h 2
5580.2.a.i 3
5580.2.a.j 3
5580.2.a.k 3
5580.2.a.l 3
5580.2.a.m 4
5580.2.a.n 4
5580.2.a.o 5
5580.2.a.p 5
5580.2.a.q 5
5580.2.a.r 5
5580.2.f \(\chi_{5580}(991, \cdot)\) n/a 320 1
5580.2.g \(\chi_{5580}(3349, \cdot)\) 5580.2.g.a 2 1
5580.2.g.b 6
5580.2.g.c 8
5580.2.g.d 14
5580.2.g.e 14
5580.2.g.f 16
5580.2.g.g 16
5580.2.h \(\chi_{5580}(4031, \cdot)\) n/a 240 1
5580.2.i \(\chi_{5580}(2789, \cdot)\) 5580.2.i.a 64 1
5580.2.n \(\chi_{5580}(1799, \cdot)\) n/a 360 1
5580.2.o \(\chi_{5580}(5021, \cdot)\) 5580.2.o.a 40 1
5580.2.p \(\chi_{5580}(4339, \cdot)\) n/a 476 1
5580.2.q \(\chi_{5580}(3601, \cdot)\) n/a 108 2
5580.2.r \(\chi_{5580}(1861, \cdot)\) n/a 240 2
5580.2.s \(\chi_{5580}(3001, \cdot)\) n/a 256 2
5580.2.t \(\chi_{5580}(1141, \cdot)\) n/a 256 2
5580.2.u \(\chi_{5580}(2357, \cdot)\) n/a 120 2
5580.2.v \(\chi_{5580}(433, \cdot)\) n/a 160 2
5580.2.w \(\chi_{5580}(3347, \cdot)\) n/a 768 2
5580.2.x \(\chi_{5580}(3907, \cdot)\) n/a 900 2
5580.2.bc \(\chi_{5580}(721, \cdot)\) n/a 208 4
5580.2.bd \(\chi_{5580}(4489, \cdot)\) n/a 384 2
5580.2.be \(\chi_{5580}(1111, \cdot)\) n/a 1536 2
5580.2.bf \(\chi_{5580}(1049, \cdot)\) n/a 384 2
5580.2.bg \(\chi_{5580}(1451, \cdot)\) n/a 1536 2
5580.2.bp \(\chi_{5580}(739, \cdot)\) n/a 952 2
5580.2.bq \(\chi_{5580}(619, \cdot)\) n/a 2288 2
5580.2.br \(\chi_{5580}(161, \cdot)\) 5580.2.br.a 88 2
5580.2.bs \(\chi_{5580}(1079, \cdot)\) n/a 768 2
5580.2.bt \(\chi_{5580}(3659, \cdot)\) n/a 2160 2
5580.2.bu \(\chi_{5580}(1301, \cdot)\) n/a 256 2
5580.2.cd \(\chi_{5580}(2599, \cdot)\) n/a 2288 2
5580.2.ce \(\chi_{5580}(2021, \cdot)\) n/a 256 2
5580.2.cf \(\chi_{5580}(2939, \cdot)\) n/a 2288 2
5580.2.ck \(\chi_{5580}(311, \cdot)\) n/a 1440 2
5580.2.cl \(\chi_{5580}(929, \cdot)\) n/a 384 2
5580.2.cm \(\chi_{5580}(3509, \cdot)\) n/a 128 2
5580.2.cn \(\chi_{5580}(2051, \cdot)\) n/a 512 2
5580.2.co \(\chi_{5580}(2851, \cdot)\) n/a 1536 2
5580.2.cp \(\chi_{5580}(1489, \cdot)\) n/a 360 2
5580.2.cq \(\chi_{5580}(1369, \cdot)\) n/a 160 2
5580.2.cr \(\chi_{5580}(1711, \cdot)\) n/a 640 2
5580.2.da \(\chi_{5580}(2909, \cdot)\) n/a 384 2
5580.2.db \(\chi_{5580}(191, \cdot)\) n/a 1536 2
5580.2.dc \(\chi_{5580}(769, \cdot)\) n/a 384 2
5580.2.dd \(\chi_{5580}(4831, \cdot)\) n/a 1536 2
5580.2.de \(\chi_{5580}(3281, \cdot)\) n/a 256 2
5580.2.df \(\chi_{5580}(1679, \cdot)\) n/a 2288 2
5580.2.dg \(\chi_{5580}(1339, \cdot)\) n/a 2288 2
5580.2.dl \(\chi_{5580}(1639, \cdot)\) n/a 1904 4
5580.2.dm \(\chi_{5580}(2321, \cdot)\) n/a 160 4
5580.2.dn \(\chi_{5580}(2519, \cdot)\) n/a 1536 4
5580.2.ds \(\chi_{5580}(89, \cdot)\) n/a 256 4
5580.2.dt \(\chi_{5580}(791, \cdot)\) n/a 1024 4
5580.2.du \(\chi_{5580}(109, \cdot)\) n/a 320 4
5580.2.dv \(\chi_{5580}(91, \cdot)\) n/a 1280 4
5580.2.ea \(\chi_{5580}(1327, \cdot)\) n/a 4576 4
5580.2.eb \(\chi_{5580}(347, \cdot)\) n/a 4576 4
5580.2.ec \(\chi_{5580}(3157, \cdot)\) n/a 768 4
5580.2.ed \(\chi_{5580}(3497, \cdot)\) n/a 768 4
5580.2.eq \(\chi_{5580}(1177, \cdot)\) n/a 768 4
5580.2.er \(\chi_{5580}(497, \cdot)\) n/a 720 4
5580.2.es \(\chi_{5580}(1927, \cdot)\) n/a 1904 4
5580.2.et \(\chi_{5580}(863, \cdot)\) n/a 1536 4
5580.2.eu \(\chi_{5580}(1607, \cdot)\) n/a 4576 4
5580.2.ev \(\chi_{5580}(67, \cdot)\) n/a 4576 4
5580.2.ew \(\chi_{5580}(893, \cdot)\) n/a 768 4
5580.2.ex \(\chi_{5580}(553, \cdot)\) n/a 768 4
5580.2.ey \(\chi_{5580}(37, \cdot)\) n/a 320 4
5580.2.ez \(\chi_{5580}(377, \cdot)\) n/a 256 4
5580.2.fa \(\chi_{5580}(187, \cdot)\) n/a 4320 4
5580.2.fb \(\chi_{5580}(743, \cdot)\) n/a 4576 4
5580.2.fg \(\chi_{5580}(661, \cdot)\) n/a 1024 8
5580.2.fh \(\chi_{5580}(121, \cdot)\) n/a 1024 8
5580.2.fi \(\chi_{5580}(481, \cdot)\) n/a 1024 8
5580.2.fj \(\chi_{5580}(361, \cdot)\) n/a 432 8
5580.2.fo \(\chi_{5580}(163, \cdot)\) n/a 3808 8
5580.2.fp \(\chi_{5580}(647, \cdot)\) n/a 3072 8
5580.2.fq \(\chi_{5580}(2197, \cdot)\) n/a 640 8
5580.2.fr \(\chi_{5580}(233, \cdot)\) n/a 512 8
5580.2.fw \(\chi_{5580}(79, \cdot)\) n/a 9152 8
5580.2.fx \(\chi_{5580}(479, \cdot)\) n/a 9152 8
5580.2.fy \(\chi_{5580}(941, \cdot)\) n/a 1024 8
5580.2.fz \(\chi_{5580}(331, \cdot)\) n/a 6144 8
5580.2.ga \(\chi_{5580}(949, \cdot)\) n/a 1536 8
5580.2.gb \(\chi_{5580}(131, \cdot)\) n/a 6144 8
5580.2.gc \(\chi_{5580}(569, \cdot)\) n/a 1536 8
5580.2.gl \(\chi_{5580}(451, \cdot)\) n/a 2560 8
5580.2.gm \(\chi_{5580}(289, \cdot)\) n/a 640 8
5580.2.gn \(\chi_{5580}(349, \cdot)\) n/a 1536 8
5580.2.go \(\chi_{5580}(151, \cdot)\) n/a 6144 8
5580.2.gp \(\chi_{5580}(71, \cdot)\) n/a 2048 8
5580.2.gq \(\chi_{5580}(269, \cdot)\) n/a 512 8
5580.2.gr \(\chi_{5580}(29, \cdot)\) n/a 1536 8
5580.2.gs \(\chi_{5580}(1031, \cdot)\) n/a 6144 8
5580.2.gx \(\chi_{5580}(59, \cdot)\) n/a 9152 8
5580.2.gy \(\chi_{5580}(641, \cdot)\) n/a 1024 8
5580.2.gz \(\chi_{5580}(259, \cdot)\) n/a 9152 8
5580.2.hi \(\chi_{5580}(401, \cdot)\) n/a 1024 8
5580.2.hj \(\chi_{5580}(419, \cdot)\) n/a 9152 8
5580.2.hk \(\chi_{5580}(359, \cdot)\) n/a 3072 8
5580.2.hl \(\chi_{5580}(881, \cdot)\) n/a 352 8
5580.2.hm \(\chi_{5580}(139, \cdot)\) n/a 9152 8
5580.2.hn \(\chi_{5580}(199, \cdot)\) n/a 3808 8
5580.2.hw \(\chi_{5580}(671, \cdot)\) n/a 6144 8
5580.2.hx \(\chi_{5580}(389, \cdot)\) n/a 1536 8
5580.2.hy \(\chi_{5580}(571, \cdot)\) n/a 6144 8
5580.2.hz \(\chi_{5580}(49, \cdot)\) n/a 1536 8
5580.2.ie \(\chi_{5580}(23, \cdot)\) n/a 18304 16
5580.2.if \(\chi_{5580}(283, \cdot)\) n/a 18304 16
5580.2.ig \(\chi_{5580}(413, \cdot)\) n/a 1024 16
5580.2.ih \(\chi_{5580}(73, \cdot)\) n/a 1280 16
5580.2.ii \(\chi_{5580}(13, \cdot)\) n/a 3072 16
5580.2.ij \(\chi_{5580}(113, \cdot)\) n/a 3072 16
5580.2.ik \(\chi_{5580}(7, \cdot)\) n/a 18304 16
5580.2.il \(\chi_{5580}(383, \cdot)\) n/a 18304 16
5580.2.im \(\chi_{5580}(323, \cdot)\) n/a 6144 16
5580.2.in \(\chi_{5580}(307, \cdot)\) n/a 7616 16
5580.2.io \(\chi_{5580}(473, \cdot)\) n/a 3072 16
5580.2.ip \(\chi_{5580}(277, \cdot)\) n/a 3072 16
5580.2.jc \(\chi_{5580}(173, \cdot)\) n/a 3072 16
5580.2.jd \(\chi_{5580}(673, \cdot)\) n/a 3072 16
5580.2.je \(\chi_{5580}(83, \cdot)\) n/a 18304 16
5580.2.jf \(\chi_{5580}(547, \cdot)\) n/a 18304 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5580))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5580)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(558))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1395))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1860))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2790))\)\(^{\oplus 2}\)