# Properties

 Label 5220.2 Level 5220 Weight 2 Dimension 305044 Nonzero newspaces 80 Sturm bound 2903040

## Defining parameters

 Level: $$N$$ = $$5220 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$2903040$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5220))$$.

Total New Old
Modular forms 734720 307956 426764
Cusp forms 716801 305044 411757
Eisenstein series 17919 2912 15007

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5220))$$

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
5220.2.a $$\chi_{5220}(1, \cdot)$$ 5220.2.a.a 1 1
5220.2.a.b 1
5220.2.a.c 1
5220.2.a.d 1
5220.2.a.e 1
5220.2.a.f 1
5220.2.a.g 1
5220.2.a.h 1
5220.2.a.i 1
5220.2.a.j 1
5220.2.a.k 1
5220.2.a.l 1
5220.2.a.m 1
5220.2.a.n 1
5220.2.a.o 1
5220.2.a.p 1
5220.2.a.q 2
5220.2.a.r 2
5220.2.a.s 2
5220.2.a.t 2
5220.2.a.u 2
5220.2.a.v 2
5220.2.a.w 3
5220.2.a.x 3
5220.2.a.y 7
5220.2.a.z 7
5220.2.b $$\chi_{5220}(289, \cdot)$$ 5220.2.b.a 4 1
5220.2.b.b 4
5220.2.b.c 14
5220.2.b.d 14
5220.2.b.e 16
5220.2.b.f 24
5220.2.e $$\chi_{5220}(3131, \cdot)$$ n/a 240 1
5220.2.g $$\chi_{5220}(2089, \cdot)$$ 5220.2.g.a 2 1
5220.2.g.b 2
5220.2.g.c 4
5220.2.g.d 10
5220.2.g.e 12
5220.2.g.f 12
5220.2.g.g 14
5220.2.g.h 14
5220.2.h $$\chi_{5220}(4931, \cdot)$$ n/a 224 1
5220.2.k $$\chi_{5220}(5219, \cdot)$$ n/a 360 1
5220.2.l $$\chi_{5220}(3421, \cdot)$$ 5220.2.l.a 2 1
5220.2.l.b 2
5220.2.l.c 2
5220.2.l.d 4
5220.2.l.e 4
5220.2.l.f 4
5220.2.l.g 4
5220.2.l.h 6
5220.2.l.i 6
5220.2.l.j 6
5220.2.l.k 10
5220.2.n $$\chi_{5220}(1799, \cdot)$$ n/a 336 1
5220.2.q $$\chi_{5220}(1741, \cdot)$$ n/a 224 2
5220.2.r $$\chi_{5220}(1351, \cdot)$$ n/a 600 2
5220.2.u $$\chi_{5220}(3149, \cdot)$$ n/a 120 2
5220.2.v $$\chi_{5220}(233, \cdot)$$ n/a 112 2
5220.2.y $$\chi_{5220}(523, \cdot)$$ n/a 840 2
5220.2.ba $$\chi_{5220}(2303, \cdot)$$ n/a 720 2
5220.2.bc $$\chi_{5220}(1873, \cdot)$$ n/a 150 2
5220.2.bd $$\chi_{5220}(2593, \cdot)$$ n/a 150 2
5220.2.bf $$\chi_{5220}(1583, \cdot)$$ n/a 720 2
5220.2.bh $$\chi_{5220}(3943, \cdot)$$ n/a 892 2
5220.2.bk $$\chi_{5220}(3653, \cdot)$$ n/a 120 2
5220.2.bl $$\chi_{5220}(1061, \cdot)$$ 5220.2.bl.a 40 2
5220.2.bl.b 40
5220.2.bo $$\chi_{5220}(3439, \cdot)$$ n/a 892 2
5220.2.bq $$\chi_{5220}(59, \cdot)$$ n/a 2016 2
5220.2.bs $$\chi_{5220}(1681, \cdot)$$ n/a 240 2
5220.2.bv $$\chi_{5220}(1739, \cdot)$$ n/a 2144 2
5220.2.bw $$\chi_{5220}(1451, \cdot)$$ n/a 1344 2
5220.2.bz $$\chi_{5220}(349, \cdot)$$ n/a 336 2
5220.2.cb $$\chi_{5220}(1391, \cdot)$$ n/a 1440 2
5220.2.cc $$\chi_{5220}(2029, \cdot)$$ n/a 360 2
5220.2.ce $$\chi_{5220}(181, \cdot)$$ n/a 300 6
5220.2.cf $$\chi_{5220}(679, \cdot)$$ n/a 4288 4
5220.2.ci $$\chi_{5220}(41, \cdot)$$ n/a 480 4
5220.2.ck $$\chi_{5220}(463, \cdot)$$ n/a 4288 4
5220.2.cl $$\chi_{5220}(173, \cdot)$$ n/a 720 4
5220.2.cn $$\chi_{5220}(563, \cdot)$$ n/a 4288 4
5220.2.cp $$\chi_{5220}(133, \cdot)$$ n/a 720 4
5220.2.cs $$\chi_{5220}(853, \cdot)$$ n/a 720 4
5220.2.cu $$\chi_{5220}(1607, \cdot)$$ n/a 4288 4
5220.2.cw $$\chi_{5220}(1973, \cdot)$$ n/a 672 4
5220.2.cx $$\chi_{5220}(2263, \cdot)$$ n/a 4032 4
5220.2.cz $$\chi_{5220}(389, \cdot)$$ n/a 720 4
5220.2.dc $$\chi_{5220}(331, \cdot)$$ n/a 2880 4
5220.2.df $$\chi_{5220}(719, \cdot)$$ n/a 2160 6
5220.2.dh $$\chi_{5220}(361, \cdot)$$ n/a 300 6
5220.2.di $$\chi_{5220}(179, \cdot)$$ n/a 2160 6
5220.2.dl $$\chi_{5220}(431, \cdot)$$ n/a 1440 6
5220.2.dm $$\chi_{5220}(1009, \cdot)$$ n/a 444 6
5220.2.do $$\chi_{5220}(71, \cdot)$$ n/a 1440 6
5220.2.dr $$\chi_{5220}(109, \cdot)$$ n/a 456 6
5220.2.ds $$\chi_{5220}(661, \cdot)$$ n/a 1440 12
5220.2.dt $$\chi_{5220}(19, \cdot)$$ n/a 5352 12
5220.2.dw $$\chi_{5220}(881, \cdot)$$ n/a 480 12
5220.2.dy $$\chi_{5220}(557, \cdot)$$ n/a 720 12
5220.2.dz $$\chi_{5220}(847, \cdot)$$ n/a 5352 12
5220.2.eb $$\chi_{5220}(37, \cdot)$$ n/a 900 12
5220.2.ed $$\chi_{5220}(143, \cdot)$$ n/a 4320 12
5220.2.eg $$\chi_{5220}(287, \cdot)$$ n/a 4320 12
5220.2.ei $$\chi_{5220}(73, \cdot)$$ n/a 900 12
5220.2.ek $$\chi_{5220}(343, \cdot)$$ n/a 5352 12
5220.2.el $$\chi_{5220}(53, \cdot)$$ n/a 720 12
5220.2.en $$\chi_{5220}(89, \cdot)$$ n/a 720 12
5220.2.eq $$\chi_{5220}(271, \cdot)$$ n/a 3600 12
5220.2.es $$\chi_{5220}(589, \cdot)$$ n/a 2160 12
5220.2.et $$\chi_{5220}(671, \cdot)$$ n/a 8640 12
5220.2.ev $$\chi_{5220}(49, \cdot)$$ n/a 2160 12
5220.2.ey $$\chi_{5220}(371, \cdot)$$ n/a 8640 12
5220.2.ez $$\chi_{5220}(299, \cdot)$$ n/a 12864 12
5220.2.fc $$\chi_{5220}(121, \cdot)$$ n/a 1440 12
5220.2.fe $$\chi_{5220}(239, \cdot)$$ n/a 12864 12
5220.2.fg $$\chi_{5220}(31, \cdot)$$ n/a 17280 24
5220.2.fj $$\chi_{5220}(329, \cdot)$$ n/a 4320 24
5220.2.fk $$\chi_{5220}(7, \cdot)$$ n/a 25728 24
5220.2.fn $$\chi_{5220}(257, \cdot)$$ n/a 4320 24
5220.2.fp $$\chi_{5220}(97, \cdot)$$ n/a 4320 24
5220.2.fr $$\chi_{5220}(443, \cdot)$$ n/a 25728 24
5220.2.fs $$\chi_{5220}(47, \cdot)$$ n/a 25728 24
5220.2.fu $$\chi_{5220}(733, \cdot)$$ n/a 4320 24
5220.2.fw $$\chi_{5220}(353, \cdot)$$ n/a 4320 24
5220.2.fz $$\chi_{5220}(67, \cdot)$$ n/a 25728 24
5220.2.ga $$\chi_{5220}(101, \cdot)$$ n/a 2880 24
5220.2.gd $$\chi_{5220}(79, \cdot)$$ n/a 25728 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5220))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5220)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(174))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(261))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(290))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(348))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(435))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(522))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(580))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(870))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1044))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1305))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1740))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2610))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5220))$$$$^{\oplus 1}$$