# Properties

 Label 5880.2 Level 5880 Weight 2 Dimension 334000 Nonzero newspaces 72 Sturm bound 3612672

## Defining parameters

 Level: $$N$$ = $$5880 = 2^{3} \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$72$$ Sturm bound: $$3612672$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5880))$$.

Total New Old
Modular forms 914688 336328 578360
Cusp forms 891649 334000 557649
Eisenstein series 23039 2328 20711

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5880))$$

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
5880.2.a $$\chi_{5880}(1, \cdot)$$ 5880.2.a.a 1 1
5880.2.a.b 1
5880.2.a.c 1
5880.2.a.d 1
5880.2.a.e 1
5880.2.a.f 1
5880.2.a.g 1
5880.2.a.h 1
5880.2.a.i 1
5880.2.a.j 1
5880.2.a.k 1
5880.2.a.l 1
5880.2.a.m 1
5880.2.a.n 1
5880.2.a.o 1
5880.2.a.p 1
5880.2.a.q 1
5880.2.a.r 1
5880.2.a.s 1
5880.2.a.t 1
5880.2.a.u 1
5880.2.a.v 1
5880.2.a.w 1
5880.2.a.x 1
5880.2.a.y 1
5880.2.a.z 1
5880.2.a.ba 1
5880.2.a.bb 1
5880.2.a.bc 1
5880.2.a.bd 1
5880.2.a.be 1
5880.2.a.bf 1
5880.2.a.bg 1
5880.2.a.bh 1
5880.2.a.bi 1
5880.2.a.bj 1
5880.2.a.bk 2
5880.2.a.bl 2
5880.2.a.bm 2
5880.2.a.bn 2
5880.2.a.bo 2
5880.2.a.bp 2
5880.2.a.bq 2
5880.2.a.br 2
5880.2.a.bs 2
5880.2.a.bt 3
5880.2.a.bu 3
5880.2.a.bv 3
5880.2.a.bw 3
5880.2.a.bx 4
5880.2.a.by 4
5880.2.a.bz 4
5880.2.a.ca 4
5880.2.d $$\chi_{5880}(391, \cdot)$$ None 0 1
5880.2.e $$\chi_{5880}(491, \cdot)$$ n/a 656 1
5880.2.f $$\chi_{5880}(881, \cdot)$$ n/a 160 1
5880.2.g $$\chi_{5880}(2941, \cdot)$$ n/a 328 1
5880.2.j $$\chi_{5880}(589, \cdot)$$ n/a 492 1
5880.2.k $$\chi_{5880}(4409, \cdot)$$ n/a 240 1
5880.2.p $$\chi_{5880}(4019, \cdot)$$ n/a 964 1
5880.2.q $$\chi_{5880}(3919, \cdot)$$ None 0 1
5880.2.t $$\chi_{5880}(3529, \cdot)$$ n/a 122 1
5880.2.u $$\chi_{5880}(1469, \cdot)$$ n/a 944 1
5880.2.v $$\chi_{5880}(1079, \cdot)$$ None 0 1
5880.2.w $$\chi_{5880}(979, \cdot)$$ n/a 480 1
5880.2.z $$\chi_{5880}(3331, \cdot)$$ n/a 320 1
5880.2.ba $$\chi_{5880}(3431, \cdot)$$ None 0 1
5880.2.bf $$\chi_{5880}(3821, \cdot)$$ n/a 640 1
5880.2.bg $$\chi_{5880}(361, \cdot)$$ n/a 160 2
5880.2.bj $$\chi_{5880}(3037, \cdot)$$ n/a 960 2
5880.2.bk $$\chi_{5880}(3137, \cdot)$$ n/a 492 2
5880.2.bl $$\chi_{5880}(2647, \cdot)$$ None 0 2
5880.2.bm $$\chi_{5880}(587, \cdot)$$ n/a 1888 2
5880.2.br $$\chi_{5880}(883, \cdot)$$ n/a 984 2
5880.2.bs $$\chi_{5880}(3527, \cdot)$$ None 0 2
5880.2.bt $$\chi_{5880}(97, \cdot)$$ n/a 240 2
5880.2.bu $$\chi_{5880}(197, \cdot)$$ n/a 1928 2
5880.2.bz $$\chi_{5880}(19, \cdot)$$ n/a 960 2
5880.2.ca $$\chi_{5880}(1439, \cdot)$$ None 0 2
5880.2.cb $$\chi_{5880}(509, \cdot)$$ n/a 1888 2
5880.2.cc $$\chi_{5880}(3889, \cdot)$$ n/a 240 2
5880.2.cf $$\chi_{5880}(2861, \cdot)$$ n/a 1280 2
5880.2.ck $$\chi_{5880}(3791, \cdot)$$ None 0 2
5880.2.cl $$\chi_{5880}(2371, \cdot)$$ n/a 640 2
5880.2.co $$\chi_{5880}(3301, \cdot)$$ n/a 640 2
5880.2.cp $$\chi_{5880}(521, \cdot)$$ n/a 320 2
5880.2.cq $$\chi_{5880}(851, \cdot)$$ n/a 1280 2
5880.2.cr $$\chi_{5880}(31, \cdot)$$ None 0 2
5880.2.cu $$\chi_{5880}(2959, \cdot)$$ None 0 2
5880.2.cv $$\chi_{5880}(4379, \cdot)$$ n/a 1888 2
5880.2.da $$\chi_{5880}(3449, \cdot)$$ n/a 480 2
5880.2.db $$\chi_{5880}(949, \cdot)$$ n/a 960 2
5880.2.dc $$\chi_{5880}(841, \cdot)$$ n/a 672 6
5880.2.dd $$\chi_{5880}(557, \cdot)$$ n/a 3776 4
5880.2.de $$\chi_{5880}(313, \cdot)$$ n/a 480 4
5880.2.dj $$\chi_{5880}(2567, \cdot)$$ None 0 4
5880.2.dk $$\chi_{5880}(67, \cdot)$$ n/a 1920 4
5880.2.dl $$\chi_{5880}(227, \cdot)$$ n/a 3776 4
5880.2.dm $$\chi_{5880}(3007, \cdot)$$ None 0 4
5880.2.dr $$\chi_{5880}(3497, \cdot)$$ n/a 960 4
5880.2.ds $$\chi_{5880}(2077, \cdot)$$ n/a 1920 4
5880.2.dv $$\chi_{5880}(461, \cdot)$$ n/a 5376 6
5880.2.dw $$\chi_{5880}(71, \cdot)$$ None 0 6
5880.2.dx $$\chi_{5880}(811, \cdot)$$ n/a 2688 6
5880.2.ea $$\chi_{5880}(139, \cdot)$$ n/a 4032 6
5880.2.eb $$\chi_{5880}(239, \cdot)$$ None 0 6
5880.2.eg $$\chi_{5880}(629, \cdot)$$ n/a 8016 6
5880.2.eh $$\chi_{5880}(169, \cdot)$$ n/a 1008 6
5880.2.ek $$\chi_{5880}(559, \cdot)$$ None 0 6
5880.2.el $$\chi_{5880}(659, \cdot)$$ n/a 8016 6
5880.2.em $$\chi_{5880}(209, \cdot)$$ n/a 2016 6
5880.2.en $$\chi_{5880}(1429, \cdot)$$ n/a 4032 6
5880.2.eq $$\chi_{5880}(421, \cdot)$$ n/a 2688 6
5880.2.er $$\chi_{5880}(41, \cdot)$$ n/a 1344 6
5880.2.ew $$\chi_{5880}(1331, \cdot)$$ n/a 5376 6
5880.2.ex $$\chi_{5880}(1231, \cdot)$$ None 0 6
5880.2.ey $$\chi_{5880}(121, \cdot)$$ n/a 1344 12
5880.2.ez $$\chi_{5880}(43, \cdot)$$ n/a 8064 12
5880.2.fa $$\chi_{5880}(167, \cdot)$$ None 0 12
5880.2.ff $$\chi_{5880}(433, \cdot)$$ n/a 2016 12
5880.2.fg $$\chi_{5880}(533, \cdot)$$ n/a 16032 12
5880.2.fh $$\chi_{5880}(13, \cdot)$$ n/a 8064 12
5880.2.fi $$\chi_{5880}(113, \cdot)$$ n/a 4032 12
5880.2.fn $$\chi_{5880}(127, \cdot)$$ None 0 12
5880.2.fo $$\chi_{5880}(83, \cdot)$$ n/a 16032 12
5880.2.fr $$\chi_{5880}(109, \cdot)$$ n/a 8064 12
5880.2.fs $$\chi_{5880}(89, \cdot)$$ n/a 4032 12
5880.2.ft $$\chi_{5880}(179, \cdot)$$ n/a 16032 12
5880.2.fu $$\chi_{5880}(199, \cdot)$$ None 0 12
5880.2.fx $$\chi_{5880}(271, \cdot)$$ None 0 12
5880.2.fy $$\chi_{5880}(11, \cdot)$$ n/a 10752 12
5880.2.gd $$\chi_{5880}(761, \cdot)$$ n/a 2688 12
5880.2.ge $$\chi_{5880}(541, \cdot)$$ n/a 5376 12
5880.2.gh $$\chi_{5880}(451, \cdot)$$ n/a 5376 12
5880.2.gi $$\chi_{5880}(191, \cdot)$$ None 0 12
5880.2.gj $$\chi_{5880}(101, \cdot)$$ n/a 10752 12
5880.2.gm $$\chi_{5880}(289, \cdot)$$ n/a 2016 12
5880.2.gn $$\chi_{5880}(269, \cdot)$$ n/a 16032 12
5880.2.gs $$\chi_{5880}(359, \cdot)$$ None 0 12
5880.2.gt $$\chi_{5880}(859, \cdot)$$ n/a 8064 12
5880.2.gw $$\chi_{5880}(467, \cdot)$$ n/a 32064 24
5880.2.gx $$\chi_{5880}(247, \cdot)$$ None 0 24
5880.2.gy $$\chi_{5880}(137, \cdot)$$ n/a 8064 24
5880.2.gz $$\chi_{5880}(157, \cdot)$$ n/a 16128 24
5880.2.he $$\chi_{5880}(53, \cdot)$$ n/a 32064 24
5880.2.hf $$\chi_{5880}(73, \cdot)$$ n/a 4032 24
5880.2.hg $$\chi_{5880}(47, \cdot)$$ None 0 24
5880.2.hh $$\chi_{5880}(163, \cdot)$$ n/a 16128 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5880))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5880)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 48}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(420))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(490))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(588))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(735))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(840))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(980))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1176))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1470))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1960))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2940))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5880))$$$$^{\oplus 1}$$