Properties

 Label 5824.2 Level 5824 Weight 2 Dimension 547372 Nonzero newspaces 140 Sturm bound 4128768

Defining parameters

 Level: $$N$$ = $$5824 = 2^{6} \cdot 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$140$$ Sturm bound: $$4128768$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5824))$$.

Total New Old
Modular forms 1042560 552212 490348
Cusp forms 1021825 547372 474453
Eisenstein series 20735 4840 15895

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5824))$$

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
5824.2.a $$\chi_{5824}(1, \cdot)$$ 5824.2.a.a 1 1
5824.2.a.b 1
5824.2.a.c 1
5824.2.a.d 1
5824.2.a.e 1
5824.2.a.f 1
5824.2.a.g 1
5824.2.a.h 1
5824.2.a.i 1
5824.2.a.j 1
5824.2.a.k 1
5824.2.a.l 1
5824.2.a.m 1
5824.2.a.n 1
5824.2.a.o 1
5824.2.a.p 1
5824.2.a.q 1
5824.2.a.r 1
5824.2.a.s 1
5824.2.a.t 1
5824.2.a.u 1
5824.2.a.v 1
5824.2.a.w 1
5824.2.a.x 1
5824.2.a.y 1
5824.2.a.z 1
5824.2.a.ba 1
5824.2.a.bb 1
5824.2.a.bc 1
5824.2.a.bd 1
5824.2.a.be 1
5824.2.a.bf 1
5824.2.a.bg 2
5824.2.a.bh 2
5824.2.a.bi 2
5824.2.a.bj 2
5824.2.a.bk 2
5824.2.a.bl 2
5824.2.a.bm 2
5824.2.a.bn 2
5824.2.a.bo 2
5824.2.a.bp 2
5824.2.a.bq 2
5824.2.a.br 2
5824.2.a.bs 3
5824.2.a.bt 3
5824.2.a.bu 3
5824.2.a.bv 3
5824.2.a.bw 3
5824.2.a.bx 3
5824.2.a.by 3
5824.2.a.bz 3
5824.2.a.ca 4
5824.2.a.cb 4
5824.2.a.cc 4
5824.2.a.cd 4
5824.2.a.ce 4
5824.2.a.cf 4
5824.2.a.cg 4
5824.2.a.ch 4
5824.2.a.ci 5
5824.2.a.cj 5
5824.2.a.ck 5
5824.2.a.cl 5
5824.2.a.cm 6
5824.2.a.cn 6
5824.2.b $$\chi_{5824}(2911, \cdot)$$ n/a 224 1
5824.2.c $$\chi_{5824}(2913, \cdot)$$ n/a 144 1
5824.2.h $$\chi_{5824}(1119, \cdot)$$ n/a 192 1
5824.2.i $$\chi_{5824}(4705, \cdot)$$ n/a 168 1
5824.2.j $$\chi_{5824}(4031, \cdot)$$ n/a 192 1
5824.2.k $$\chi_{5824}(1793, \cdot)$$ n/a 168 1
5824.2.p $$\chi_{5824}(5823, \cdot)$$ n/a 220 1
5824.2.q $$\chi_{5824}(1985, \cdot)$$ n/a 440 2
5824.2.r $$\chi_{5824}(3329, \cdot)$$ n/a 384 2
5824.2.s $$\chi_{5824}(4033, \cdot)$$ n/a 336 2
5824.2.t $$\chi_{5824}(1537, \cdot)$$ n/a 440 2
5824.2.v $$\chi_{5824}(1919, \cdot)$$ n/a 336 2
5824.2.w $$\chi_{5824}(1217, \cdot)$$ n/a 440 2
5824.2.y $$\chi_{5824}(239, \cdot)$$ n/a 336 2
5824.2.z $$\chi_{5824}(5361, \cdot)$$ n/a 440 2
5824.2.bd $$\chi_{5824}(2575, \cdot)$$ n/a 384 2
5824.2.be $$\chi_{5824}(337, \cdot)$$ n/a 336 2
5824.2.bh $$\chi_{5824}(1455, \cdot)$$ n/a 440 2
5824.2.bi $$\chi_{5824}(1457, \cdot)$$ n/a 288 2
5824.2.bm $$\chi_{5824}(3151, \cdot)$$ n/a 336 2
5824.2.bn $$\chi_{5824}(2449, \cdot)$$ n/a 440 2
5824.2.bp $$\chi_{5824}(1695, \cdot)$$ n/a 336 2
5824.2.bq $$\chi_{5824}(993, \cdot)$$ n/a 448 2
5824.2.bu $$\chi_{5824}(4001, \cdot)$$ n/a 448 2
5824.2.bv $$\chi_{5824}(607, \cdot)$$ n/a 448 2
5824.2.bw $$\chi_{5824}(737, \cdot)$$ n/a 448 2
5824.2.bx $$\chi_{5824}(1375, \cdot)$$ n/a 448 2
5824.2.cc $$\chi_{5824}(3137, \cdot)$$ n/a 336 2
5824.2.cd $$\chi_{5824}(2239, \cdot)$$ n/a 440 2
5824.2.ce $$\chi_{5824}(2623, \cdot)$$ n/a 440 2
5824.2.cf $$\chi_{5824}(831, \cdot)$$ n/a 440 2
5824.2.co $$\chi_{5824}(961, \cdot)$$ n/a 440 2
5824.2.cp $$\chi_{5824}(703, \cdot)$$ n/a 384 2
5824.2.cq $$\chi_{5824}(3071, \cdot)$$ n/a 440 2
5824.2.cr $$\chi_{5824}(641, \cdot)$$ n/a 440 2
5824.2.cs $$\chi_{5824}(1343, \cdot)$$ n/a 440 2
5824.2.cx $$\chi_{5824}(1121, \cdot)$$ n/a 336 2
5824.2.cy $$\chi_{5824}(4255, \cdot)$$ n/a 448 2
5824.2.cz $$\chi_{5824}(2209, \cdot)$$ n/a 448 2
5824.2.da $$\chi_{5824}(1951, \cdot)$$ n/a 384 2
5824.2.db $$\chi_{5824}(159, \cdot)$$ n/a 448 2
5824.2.dc $$\chi_{5824}(3553, \cdot)$$ n/a 448 2
5824.2.dl $$\chi_{5824}(927, \cdot)$$ n/a 448 2
5824.2.dm $$\chi_{5824}(289, \cdot)$$ n/a 448 2
5824.2.dn $$\chi_{5824}(417, \cdot)$$ n/a 384 2
5824.2.do $$\chi_{5824}(3743, \cdot)$$ n/a 448 2
5824.2.dp $$\chi_{5824}(225, \cdot)$$ n/a 336 2
5824.2.dq $$\chi_{5824}(5151, \cdot)$$ n/a 448 2
5824.2.dv $$\chi_{5824}(2175, \cdot)$$ n/a 440 2
5824.2.dw $$\chi_{5824}(1089, \cdot)$$ n/a 440 2
5824.2.dx $$\chi_{5824}(3519, \cdot)$$ n/a 440 2
5824.2.eb $$\chi_{5824}(729, \cdot)$$ None 0 4
5824.2.ed $$\chi_{5824}(727, \cdot)$$ None 0 4
5824.2.ee $$\chi_{5824}(265, \cdot)$$ None 0 4
5824.2.eh $$\chi_{5824}(489, \cdot)$$ None 0 4
5824.2.ei $$\chi_{5824}(967, \cdot)$$ None 0 4
5824.2.el $$\chi_{5824}(1191, \cdot)$$ None 0 4
5824.2.em $$\chi_{5824}(1065, \cdot)$$ None 0 4
5824.2.eo $$\chi_{5824}(391, \cdot)$$ None 0 4
5824.2.er $$\chi_{5824}(1025, \cdot)$$ n/a 880 4
5824.2.es $$\chi_{5824}(1983, \cdot)$$ n/a 880 4
5824.2.ev $$\chi_{5824}(1311, \cdot)$$ n/a 896 4
5824.2.ey $$\chi_{5824}(97, \cdot)$$ n/a 896 4
5824.2.ez $$\chi_{5824}(801, \cdot)$$ n/a 896 4
5824.2.fa $$\chi_{5824}(799, \cdot)$$ n/a 672 4
5824.2.fb $$\chi_{5824}(863, \cdot)$$ n/a 896 4
5824.2.fe $$\chi_{5824}(1697, \cdot)$$ n/a 896 4
5824.2.fi $$\chi_{5824}(657, \cdot)$$ n/a 880 4
5824.2.fj $$\chi_{5824}(1359, \cdot)$$ n/a 672 4
5824.2.fm $$\chi_{5824}(1809, \cdot)$$ n/a 880 4
5824.2.fn $$\chi_{5824}(1423, \cdot)$$ n/a 880 4
5824.2.fo $$\chi_{5824}(1775, \cdot)$$ n/a 880 4
5824.2.fp $$\chi_{5824}(3281, \cdot)$$ n/a 880 4
5824.2.fq $$\chi_{5824}(655, \cdot)$$ n/a 880 4
5824.2.fr $$\chi_{5824}(145, \cdot)$$ n/a 880 4
5824.2.fx $$\chi_{5824}(81, \cdot)$$ n/a 880 4
5824.2.fy $$\chi_{5824}(719, \cdot)$$ n/a 880 4
5824.2.gb $$\chi_{5824}(849, \cdot)$$ n/a 880 4
5824.2.gc $$\chi_{5824}(367, \cdot)$$ n/a 880 4
5824.2.gf $$\chi_{5824}(753, \cdot)$$ n/a 880 4
5824.2.gg $$\chi_{5824}(495, \cdot)$$ n/a 768 4
5824.2.gj $$\chi_{5824}(1167, \cdot)$$ n/a 880 4
5824.2.gl $$\chi_{5824}(113, \cdot)$$ n/a 672 4
5824.2.gm $$\chi_{5824}(335, \cdot)$$ n/a 880 4
5824.2.go $$\chi_{5824}(529, \cdot)$$ n/a 880 4
5824.2.gr $$\chi_{5824}(815, \cdot)$$ n/a 880 4
5824.2.gt $$\chi_{5824}(1681, \cdot)$$ n/a 672 4
5824.2.gu $$\chi_{5824}(783, \cdot)$$ n/a 880 4
5824.2.gw $$\chi_{5824}(1297, \cdot)$$ n/a 880 4
5824.2.gz $$\chi_{5824}(625, \cdot)$$ n/a 768 4
5824.2.ha $$\chi_{5824}(1039, \cdot)$$ n/a 880 4
5824.2.hc $$\chi_{5824}(1489, \cdot)$$ n/a 880 4
5824.2.hd $$\chi_{5824}(431, \cdot)$$ n/a 880 4
5824.2.hk $$\chi_{5824}(2095, \cdot)$$ n/a 880 4
5824.2.hl $$\chi_{5824}(369, \cdot)$$ n/a 880 4
5824.2.hm $$\chi_{5824}(3567, \cdot)$$ n/a 880 4
5824.2.hn $$\chi_{5824}(1137, \cdot)$$ n/a 880 4
5824.2.ho $$\chi_{5824}(1553, \cdot)$$ n/a 880 4
5824.2.hp $$\chi_{5824}(15, \cdot)$$ n/a 672 4
5824.2.ht $$\chi_{5824}(319, \cdot)$$ n/a 880 4
5824.2.hw $$\chi_{5824}(769, \cdot)$$ n/a 880 4
5824.2.hx $$\chi_{5824}(577, \cdot)$$ n/a 880 4
5824.2.hy $$\chi_{5824}(1471, \cdot)$$ n/a 672 4
5824.2.hz $$\chi_{5824}(1087, \cdot)$$ n/a 880 4
5824.2.ic $$\chi_{5824}(1601, \cdot)$$ n/a 880 4
5824.2.if $$\chi_{5824}(33, \cdot)$$ n/a 896 4
5824.2.ig $$\chi_{5824}(1887, \cdot)$$ n/a 896 4
5824.2.ii $$\chi_{5824}(99, \cdot)$$ n/a 5376 8
5824.2.il $$\chi_{5824}(853, \cdot)$$ n/a 7136 8
5824.2.in $$\chi_{5824}(365, \cdot)$$ n/a 4608 8
5824.2.io $$\chi_{5824}(27, \cdot)$$ n/a 6144 8
5824.2.iq $$\chi_{5824}(363, \cdot)$$ n/a 7136 8
5824.2.it $$\chi_{5824}(701, \cdot)$$ n/a 5376 8
5824.2.iv $$\chi_{5824}(125, \cdot)$$ n/a 7136 8
5824.2.iw $$\chi_{5824}(827, \cdot)$$ n/a 5376 8
5824.2.iy $$\chi_{5824}(103, \cdot)$$ None 0 8
5824.2.ja $$\chi_{5824}(1145, \cdot)$$ None 0 8
5824.2.jd $$\chi_{5824}(569, \cdot)$$ None 0 8
5824.2.je $$\chi_{5824}(1095, \cdot)$$ None 0 8
5824.2.jh $$\chi_{5824}(55, \cdot)$$ None 0 8
5824.2.jj $$\chi_{5824}(953, \cdot)$$ None 0 8
5824.2.jk $$\chi_{5824}(121, \cdot)$$ None 0 8
5824.2.jn $$\chi_{5824}(87, \cdot)$$ None 0 8
5824.2.jo $$\chi_{5824}(409, \cdot)$$ None 0 8
5824.2.jr $$\chi_{5824}(89, \cdot)$$ None 0 8
5824.2.js $$\chi_{5824}(135, \cdot)$$ None 0 8
5824.2.ju $$\chi_{5824}(1415, \cdot)$$ None 0 8
5824.2.jv $$\chi_{5824}(695, \cdot)$$ None 0 8
5824.2.ka $$\chi_{5824}(375, \cdot)$$ None 0 8
5824.2.kb $$\chi_{5824}(71, \cdot)$$ None 0 8
5824.2.kd $$\chi_{5824}(359, \cdot)$$ None 0 8
5824.2.ke $$\chi_{5824}(1097, \cdot)$$ None 0 8
5824.2.kg $$\chi_{5824}(713, \cdot)$$ None 0 8
5824.2.kh $$\chi_{5824}(297, \cdot)$$ None 0 8
5824.2.km $$\chi_{5824}(201, \cdot)$$ None 0 8
5824.2.kn $$\chi_{5824}(41, \cdot)$$ None 0 8
5824.2.kp $$\chi_{5824}(73, \cdot)$$ None 0 8
5824.2.kq $$\chi_{5824}(583, \cdot)$$ None 0 8
5824.2.kt $$\chi_{5824}(487, \cdot)$$ None 0 8
5824.2.ku $$\chi_{5824}(1017, \cdot)$$ None 0 8
5824.2.kw $$\chi_{5824}(615, \cdot)$$ None 0 8
5824.2.kz $$\chi_{5824}(647, \cdot)$$ None 0 8
5824.2.lb $$\chi_{5824}(9, \cdot)$$ None 0 8
5824.2.lc $$\chi_{5824}(393, \cdot)$$ None 0 8
5824.2.le $$\chi_{5824}(199, \cdot)$$ None 0 8
5824.2.lh $$\chi_{5824}(1223, \cdot)$$ None 0 8
5824.2.lj $$\chi_{5824}(25, \cdot)$$ None 0 8
5824.2.lk $$\chi_{5824}(229, \cdot)$$ n/a 14272 16
5824.2.ln $$\chi_{5824}(515, \cdot)$$ n/a 14272 16
5824.2.lo $$\chi_{5824}(349, \cdot)$$ n/a 14272 16
5824.2.lq $$\chi_{5824}(219, \cdot)$$ n/a 14272 16
5824.2.ls $$\chi_{5824}(11, \cdot)$$ n/a 14272 16
5824.2.lv $$\chi_{5824}(397, \cdot)$$ n/a 14272 16
5824.2.lx $$\chi_{5824}(605, \cdot)$$ n/a 14272 16
5824.2.lz $$\chi_{5824}(267, \cdot)$$ n/a 10752 16
5824.2.ma $$\chi_{5824}(139, \cdot)$$ n/a 14272 16
5824.2.md $$\chi_{5824}(29, \cdot)$$ n/a 10752 16
5824.2.mf $$\chi_{5824}(283, \cdot)$$ n/a 14272 16
5824.2.mg $$\chi_{5824}(205, \cdot)$$ n/a 14272 16
5824.2.mi $$\chi_{5824}(389, \cdot)$$ n/a 14272 16
5824.2.ml $$\chi_{5824}(467, \cdot)$$ n/a 14272 16
5824.2.mn $$\chi_{5824}(75, \cdot)$$ n/a 14272 16
5824.2.mo $$\chi_{5824}(485, \cdot)$$ n/a 14272 16
5824.2.mq $$\chi_{5824}(373, \cdot)$$ n/a 14272 16
5824.2.mt $$\chi_{5824}(131, \cdot)$$ n/a 12288 16
5824.2.mv $$\chi_{5824}(451, \cdot)$$ n/a 14272 16
5824.2.mw $$\chi_{5824}(165, \cdot)$$ n/a 14272 16
5824.2.my $$\chi_{5824}(53, \cdot)$$ n/a 12288 16
5824.2.nb $$\chi_{5824}(3, \cdot)$$ n/a 14272 16
5824.2.nd $$\chi_{5824}(309, \cdot)$$ n/a 10752 16
5824.2.ne $$\chi_{5824}(251, \cdot)$$ n/a 14272 16
5824.2.nh $$\chi_{5824}(323, \cdot)$$ n/a 10752 16
5824.2.nj $$\chi_{5824}(661, \cdot)$$ n/a 14272 16
5824.2.nl $$\chi_{5824}(45, \cdot)$$ n/a 14272 16
5824.2.nm $$\chi_{5824}(123, \cdot)$$ n/a 14272 16
5824.2.no $$\chi_{5824}(163, \cdot)$$ n/a 14272 16
5824.2.nq $$\chi_{5824}(293, \cdot)$$ n/a 14272 16
5824.2.nt $$\chi_{5824}(291, \cdot)$$ n/a 14272 16
5824.2.nu $$\chi_{5824}(5, \cdot)$$ n/a 14272 16

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5824))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5824)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(728))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(832))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1456))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2912))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5824))$$$$^{\oplus 1}$$