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Properties

Label 5520.2
Level 5520
Weight 2
Dimension 311312
Nonzero newspaces 56
Sturm bound 3244032

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Defining parameters

Level: \( N \) = \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(3244032\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5520))\).

Total New Old
Modular forms 820864 313576 507288
Cusp forms 801153 311312 489841
Eisenstein series 19711 2264 17447

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5520))\)

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
5520.2.a \(\chi_{5520}(1, \cdot)\) 5520.2.a.a 1 1
5520.2.a.b 1
5520.2.a.c 1
5520.2.a.d 1
5520.2.a.e 1
5520.2.a.f 1
5520.2.a.g 1
5520.2.a.h 1
5520.2.a.i 1
5520.2.a.j 1
5520.2.a.k 1
5520.2.a.l 1
5520.2.a.m 1
5520.2.a.n 1
5520.2.a.o 1
5520.2.a.p 1
5520.2.a.q 1
5520.2.a.r 1
5520.2.a.s 1
5520.2.a.t 1
5520.2.a.u 1
5520.2.a.v 1
5520.2.a.w 1
5520.2.a.x 1
5520.2.a.y 1
5520.2.a.z 1
5520.2.a.ba 1
5520.2.a.bb 1
5520.2.a.bc 1
5520.2.a.bd 1
5520.2.a.be 1
5520.2.a.bf 1
5520.2.a.bg 1
5520.2.a.bh 2
5520.2.a.bi 2
5520.2.a.bj 2
5520.2.a.bk 2
5520.2.a.bl 2
5520.2.a.bm 2
5520.2.a.bn 2
5520.2.a.bo 2
5520.2.a.bp 2
5520.2.a.bq 2
5520.2.a.br 2
5520.2.a.bs 2
5520.2.a.bt 2
5520.2.a.bu 2
5520.2.a.bv 3
5520.2.a.bw 3
5520.2.a.bx 3
5520.2.a.by 3
5520.2.a.bz 3
5520.2.a.ca 3
5520.2.a.cb 4
5520.2.a.cc 5
5520.2.c \(\chi_{5520}(3911, \cdot)\) None 0 1
5520.2.e \(\chi_{5520}(1241, \cdot)\) None 0 1
5520.2.f \(\chi_{5520}(4969, \cdot)\) None 0 1
5520.2.h \(\chi_{5520}(919, \cdot)\) None 0 1
5520.2.k \(\chi_{5520}(2209, \cdot)\) n/a 132 1
5520.2.m \(\chi_{5520}(3679, \cdot)\) n/a 144 1
5520.2.n \(\chi_{5520}(1151, \cdot)\) n/a 176 1
5520.2.p \(\chi_{5520}(4001, \cdot)\) n/a 192 1
5520.2.r \(\chi_{5520}(4231, \cdot)\) None 0 1
5520.2.t \(\chi_{5520}(2761, \cdot)\) None 0 1
5520.2.w \(\chi_{5520}(3449, \cdot)\) None 0 1
5520.2.y \(\chi_{5520}(599, \cdot)\) None 0 1
5520.2.z \(\chi_{5520}(689, \cdot)\) n/a 284 1
5520.2.bb \(\chi_{5520}(3359, \cdot)\) n/a 264 1
5520.2.be \(\chi_{5520}(1471, \cdot)\) 5520.2.be.a 16 1
5520.2.be.b 16
5520.2.be.c 32
5520.2.be.d 32
5520.2.bg \(\chi_{5520}(91, \cdot)\) n/a 768 2
5520.2.bj \(\chi_{5520}(2069, \cdot)\) n/a 2288 2
5520.2.bk \(\chi_{5520}(1979, \cdot)\) n/a 2112 2
5520.2.bn \(\chi_{5520}(1381, \cdot)\) n/a 704 2
5520.2.bq \(\chi_{5520}(1103, \cdot)\) n/a 576 2
5520.2.br \(\chi_{5520}(737, \cdot)\) n/a 528 2
5520.2.bs \(\chi_{5520}(2623, \cdot)\) n/a 264 2
5520.2.bt \(\chi_{5520}(1057, \cdot)\) n/a 288 2
5520.2.bw \(\chi_{5520}(2347, \cdot)\) n/a 1056 2
5520.2.bz \(\chi_{5520}(827, \cdot)\) n/a 2288 2
5520.2.cb \(\chi_{5520}(2117, \cdot)\) n/a 2112 2
5520.2.cc \(\chi_{5520}(2437, \cdot)\) n/a 1152 2
5520.2.cf \(\chi_{5520}(3587, \cdot)\) n/a 2288 2
5520.2.cg \(\chi_{5520}(1243, \cdot)\) n/a 1056 2
5520.2.ci \(\chi_{5520}(1333, \cdot)\) n/a 1152 2
5520.2.cl \(\chi_{5520}(1013, \cdot)\) n/a 2112 2
5520.2.co \(\chi_{5520}(967, \cdot)\) None 0 2
5520.2.cp \(\chi_{5520}(2713, \cdot)\) None 0 2
5520.2.cq \(\chi_{5520}(3863, \cdot)\) None 0 2
5520.2.cr \(\chi_{5520}(2393, \cdot)\) None 0 2
5520.2.cv \(\chi_{5520}(2531, \cdot)\) n/a 1408 2
5520.2.cw \(\chi_{5520}(829, \cdot)\) n/a 1056 2
5520.2.cz \(\chi_{5520}(2299, \cdot)\) n/a 1152 2
5520.2.da \(\chi_{5520}(2621, \cdot)\) n/a 1536 2
5520.2.dc \(\chi_{5520}(721, \cdot)\) n/a 960 10
5520.2.de \(\chi_{5520}(511, \cdot)\) n/a 960 10
5520.2.dh \(\chi_{5520}(239, \cdot)\) n/a 2880 10
5520.2.dj \(\chi_{5520}(1169, \cdot)\) n/a 2840 10
5520.2.dk \(\chi_{5520}(119, \cdot)\) None 0 10
5520.2.dm \(\chi_{5520}(89, \cdot)\) None 0 10
5520.2.dp \(\chi_{5520}(121, \cdot)\) None 0 10
5520.2.dr \(\chi_{5520}(631, \cdot)\) None 0 10
5520.2.dt \(\chi_{5520}(401, \cdot)\) n/a 1920 10
5520.2.dv \(\chi_{5520}(671, \cdot)\) n/a 1920 10
5520.2.dw \(\chi_{5520}(79, \cdot)\) n/a 1440 10
5520.2.dy \(\chi_{5520}(49, \cdot)\) n/a 1440 10
5520.2.eb \(\chi_{5520}(199, \cdot)\) None 0 10
5520.2.ed \(\chi_{5520}(169, \cdot)\) None 0 10
5520.2.ee \(\chi_{5520}(281, \cdot)\) None 0 10
5520.2.eg \(\chi_{5520}(71, \cdot)\) None 0 10
5520.2.ei \(\chi_{5520}(221, \cdot)\) n/a 15360 20
5520.2.el \(\chi_{5520}(19, \cdot)\) n/a 11520 20
5520.2.em \(\chi_{5520}(349, \cdot)\) n/a 11520 20
5520.2.ep \(\chi_{5520}(131, \cdot)\) n/a 15360 20
5520.2.es \(\chi_{5520}(233, \cdot)\) None 0 20
5520.2.et \(\chi_{5520}(263, \cdot)\) None 0 20
5520.2.eu \(\chi_{5520}(217, \cdot)\) None 0 20
5520.2.ev \(\chi_{5520}(487, \cdot)\) None 0 20
5520.2.ey \(\chi_{5520}(77, \cdot)\) n/a 22880 20
5520.2.fb \(\chi_{5520}(157, \cdot)\) n/a 11520 20
5520.2.fd \(\chi_{5520}(307, \cdot)\) n/a 11520 20
5520.2.fe \(\chi_{5520}(203, \cdot)\) n/a 22880 20
5520.2.fh \(\chi_{5520}(37, \cdot)\) n/a 11520 20
5520.2.fi \(\chi_{5520}(173, \cdot)\) n/a 22880 20
5520.2.fk \(\chi_{5520}(83, \cdot)\) n/a 22880 20
5520.2.fn \(\chi_{5520}(163, \cdot)\) n/a 11520 20
5520.2.fq \(\chi_{5520}(97, \cdot)\) n/a 2880 20
5520.2.fr \(\chi_{5520}(127, \cdot)\) n/a 2880 20
5520.2.fs \(\chi_{5520}(257, \cdot)\) n/a 5680 20
5520.2.ft \(\chi_{5520}(143, \cdot)\) n/a 5760 20
5520.2.fx \(\chi_{5520}(301, \cdot)\) n/a 7680 20
5520.2.fy \(\chi_{5520}(59, \cdot)\) n/a 22880 20
5520.2.gb \(\chi_{5520}(149, \cdot)\) n/a 22880 20
5520.2.gc \(\chi_{5520}(451, \cdot)\) n/a 7680 20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5520))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5520)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2760))\)\(^{\oplus 2}\)