Properties

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

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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 the 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

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