# Properties

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

## 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

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