Properties

Label 5328.2
Level 5328
Weight 2
Dimension 348962
Nonzero newspaces 112
Sturm bound 3151872

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Defining parameters

Level: \( N \) = \( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 112 \)
Sturm bound: \(3151872\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5328))\).

Total New Old
Modular forms 796032 351796 444236
Cusp forms 779905 348962 430943
Eisenstein series 16127 2834 13293

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5328))\)

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
5328.2.a \(\chi_{5328}(1, \cdot)\) 5328.2.a.a 1 1
5328.2.a.b 1
5328.2.a.c 1
5328.2.a.d 1
5328.2.a.e 1
5328.2.a.f 1
5328.2.a.g 1
5328.2.a.h 1
5328.2.a.i 1
5328.2.a.j 1
5328.2.a.k 1
5328.2.a.l 1
5328.2.a.m 1
5328.2.a.n 1
5328.2.a.o 1
5328.2.a.p 1
5328.2.a.q 1
5328.2.a.r 1
5328.2.a.s 1
5328.2.a.t 1
5328.2.a.u 1
5328.2.a.v 1
5328.2.a.w 1
5328.2.a.x 1
5328.2.a.y 2
5328.2.a.z 2
5328.2.a.ba 2
5328.2.a.bb 2
5328.2.a.bc 2
5328.2.a.bd 2
5328.2.a.be 2
5328.2.a.bf 2
5328.2.a.bg 2
5328.2.a.bh 2
5328.2.a.bi 2
5328.2.a.bj 3
5328.2.a.bk 3
5328.2.a.bl 3
5328.2.a.bm 3
5328.2.a.bn 3
5328.2.a.bo 3
5328.2.a.bp 4
5328.2.a.bq 4
5328.2.a.br 4
5328.2.a.bs 4
5328.2.a.bt 5
5328.2.a.bu 5
5328.2.c \(\chi_{5328}(2663, \cdot)\) None 0 1
5328.2.e \(\chi_{5328}(2591, \cdot)\) 5328.2.e.a 2 1
5328.2.e.b 2
5328.2.e.c 4
5328.2.e.d 4
5328.2.e.e 12
5328.2.e.f 24
5328.2.e.g 24
5328.2.f \(\chi_{5328}(2665, \cdot)\) None 0 1
5328.2.h \(\chi_{5328}(2737, \cdot)\) 5328.2.h.a 2 1
5328.2.h.b 2
5328.2.h.c 2
5328.2.h.d 2
5328.2.h.e 2
5328.2.h.f 2
5328.2.h.g 4
5328.2.h.h 4
5328.2.h.i 4
5328.2.h.j 4
5328.2.h.k 4
5328.2.h.l 4
5328.2.h.m 4
5328.2.h.n 6
5328.2.h.o 8
5328.2.h.p 10
5328.2.h.q 10
5328.2.h.r 20
5328.2.j \(\chi_{5328}(5255, \cdot)\) None 0 1
5328.2.l \(\chi_{5328}(5327, \cdot)\) 5328.2.l.a 4 1
5328.2.l.b 4
5328.2.l.c 4
5328.2.l.d 8
5328.2.l.e 8
5328.2.l.f 48
5328.2.o \(\chi_{5328}(73, \cdot)\) None 0 1
5328.2.q \(\chi_{5328}(1777, \cdot)\) n/a 432 2
5328.2.r \(\chi_{5328}(433, \cdot)\) n/a 188 2
5328.2.s \(\chi_{5328}(2209, \cdot)\) n/a 452 2
5328.2.t \(\chi_{5328}(2785, \cdot)\) n/a 452 2
5328.2.u \(\chi_{5328}(413, \cdot)\) n/a 608 2
5328.2.x \(\chi_{5328}(1819, \cdot)\) n/a 756 2
5328.2.y \(\chi_{5328}(487, \cdot)\) None 0 2
5328.2.ba \(\chi_{5328}(1405, \cdot)\) n/a 756 2
5328.2.bd \(\chi_{5328}(1333, \cdot)\) n/a 720 2
5328.2.be \(\chi_{5328}(3151, \cdot)\) n/a 190 2
5328.2.bh \(\chi_{5328}(4409, \cdot)\) None 0 2
5328.2.bi \(\chi_{5328}(1259, \cdot)\) n/a 576 2
5328.2.bl \(\chi_{5328}(1331, \cdot)\) n/a 608 2
5328.2.bn \(\chi_{5328}(1745, \cdot)\) n/a 152 2
5328.2.bp \(\chi_{5328}(845, \cdot)\) n/a 608 2
5328.2.bq \(\chi_{5328}(2251, \cdot)\) n/a 756 2
5328.2.bs \(\chi_{5328}(529, \cdot)\) n/a 452 2
5328.2.bu \(\chi_{5328}(121, \cdot)\) None 0 2
5328.2.bx \(\chi_{5328}(1823, \cdot)\) n/a 456 2
5328.2.bz \(\chi_{5328}(4007, \cdot)\) None 0 2
5328.2.cb \(\chi_{5328}(767, \cdot)\) n/a 456 2
5328.2.cd \(\chi_{5328}(2711, \cdot)\) None 0 2
5328.2.ce \(\chi_{5328}(4393, \cdot)\) None 0 2
5328.2.ch \(\chi_{5328}(1849, \cdot)\) None 0 2
5328.2.cl \(\chi_{5328}(359, \cdot)\) None 0 2
5328.2.cn \(\chi_{5328}(1775, \cdot)\) n/a 456 2
5328.2.cp \(\chi_{5328}(1703, \cdot)\) None 0 2
5328.2.cr \(\chi_{5328}(4319, \cdot)\) n/a 152 2
5328.2.ct \(\chi_{5328}(1417, \cdot)\) None 0 2
5328.2.cv \(\chi_{5328}(47, \cdot)\) n/a 456 2
5328.2.cx \(\chi_{5328}(455, \cdot)\) None 0 2
5328.2.da \(\chi_{5328}(3097, \cdot)\) None 0 2
5328.2.dc \(\chi_{5328}(961, \cdot)\) n/a 452 2
5328.2.de \(\chi_{5328}(889, \cdot)\) None 0 2
5328.2.dg \(\chi_{5328}(1729, \cdot)\) n/a 188 2
5328.2.dh \(\chi_{5328}(1655, \cdot)\) None 0 2
5328.2.dj \(\chi_{5328}(815, \cdot)\) n/a 432 2
5328.2.dl \(\chi_{5328}(887, \cdot)\) None 0 2
5328.2.dn \(\chi_{5328}(3023, \cdot)\) n/a 152 2
5328.2.dq \(\chi_{5328}(4081, \cdot)\) n/a 452 2
5328.2.ds \(\chi_{5328}(1897, \cdot)\) None 0 2
5328.2.dv \(\chi_{5328}(841, \cdot)\) None 0 2
5328.2.dw \(\chi_{5328}(1343, \cdot)\) n/a 456 2
5328.2.dy \(\chi_{5328}(2135, \cdot)\) None 0 2
5328.2.ea \(\chi_{5328}(49, \cdot)\) n/a 1356 6
5328.2.eb \(\chi_{5328}(145, \cdot)\) n/a 564 6
5328.2.ec \(\chi_{5328}(625, \cdot)\) n/a 1356 6
5328.2.ee \(\chi_{5328}(547, \cdot)\) n/a 3632 4
5328.2.ef \(\chi_{5328}(1013, \cdot)\) n/a 3632 4
5328.2.eh \(\chi_{5328}(245, \cdot)\) n/a 3632 4
5328.2.el \(\chi_{5328}(1531, \cdot)\) n/a 1512 4
5328.2.em \(\chi_{5328}(475, \cdot)\) n/a 3632 4
5328.2.en \(\chi_{5328}(125, \cdot)\) n/a 1216 4
5328.2.eo \(\chi_{5328}(1301, \cdot)\) n/a 3632 4
5328.2.es \(\chi_{5328}(1435, \cdot)\) n/a 3632 4
5328.2.eu \(\chi_{5328}(1087, \cdot)\) n/a 912 4
5328.2.ev \(\chi_{5328}(565, \cdot)\) n/a 3632 4
5328.2.ey \(\chi_{5328}(85, \cdot)\) n/a 3632 4
5328.2.fa \(\chi_{5328}(103, \cdot)\) None 0 4
5328.2.fb \(\chi_{5328}(1673, \cdot)\) None 0 4
5328.2.fe \(\chi_{5328}(689, \cdot)\) n/a 904 4
5328.2.ff \(\chi_{5328}(401, \cdot)\) n/a 904 4
5328.2.fi \(\chi_{5328}(371, \cdot)\) n/a 3456 4
5328.2.fj \(\chi_{5328}(11, \cdot)\) n/a 3632 4
5328.2.fm \(\chi_{5328}(323, \cdot)\) n/a 1216 4
5328.2.fn \(\chi_{5328}(1691, \cdot)\) n/a 1216 4
5328.2.fq \(\chi_{5328}(491, \cdot)\) n/a 3632 4
5328.2.fr \(\chi_{5328}(443, \cdot)\) n/a 3632 4
5328.2.fu \(\chi_{5328}(2345, \cdot)\) None 0 4
5328.2.fv \(\chi_{5328}(857, \cdot)\) None 0 4
5328.2.fx \(\chi_{5328}(1457, \cdot)\) n/a 304 4
5328.2.ga \(\chi_{5328}(199, \cdot)\) None 0 4
5328.2.gb \(\chi_{5328}(319, \cdot)\) n/a 912 4
5328.2.ge \(\chi_{5328}(31, \cdot)\) n/a 912 4
5328.2.gg \(\chi_{5328}(517, \cdot)\) n/a 3632 4
5328.2.gi \(\chi_{5328}(1765, \cdot)\) n/a 1512 4
5328.2.gj \(\chi_{5328}(1453, \cdot)\) n/a 3632 4
5328.2.gm \(\chi_{5328}(1861, \cdot)\) n/a 3632 4
5328.2.gn \(\chi_{5328}(397, \cdot)\) n/a 1512 4
5328.2.gp \(\chi_{5328}(445, \cdot)\) n/a 3456 4
5328.2.gr \(\chi_{5328}(1303, \cdot)\) None 0 4
5328.2.gu \(\chi_{5328}(2263, \cdot)\) None 0 4
5328.2.gw \(\chi_{5328}(415, \cdot)\) n/a 380 4
5328.2.gx \(\chi_{5328}(2561, \cdot)\) n/a 904 4
5328.2.gz \(\chi_{5328}(1787, \cdot)\) n/a 3632 4
5328.2.hc \(\chi_{5328}(1379, \cdot)\) n/a 3632 4
5328.2.hd \(\chi_{5328}(473, \cdot)\) None 0 4
5328.2.hg \(\chi_{5328}(1229, \cdot)\) n/a 3632 4
5328.2.hh \(\chi_{5328}(43, \cdot)\) n/a 3632 4
5328.2.hi \(\chi_{5328}(2323, \cdot)\) n/a 1512 4
5328.2.hn \(\chi_{5328}(1733, \cdot)\) n/a 3632 4
5328.2.ho \(\chi_{5328}(917, \cdot)\) n/a 1216 4
5328.2.hp \(\chi_{5328}(763, \cdot)\) n/a 3632 4
5328.2.hr \(\chi_{5328}(1651, \cdot)\) n/a 3632 4
5328.2.hu \(\chi_{5328}(29, \cdot)\) n/a 3632 4
5328.2.hw \(\chi_{5328}(743, \cdot)\) None 0 6
5328.2.hx \(\chi_{5328}(25, \cdot)\) None 0 6
5328.2.ia \(\chi_{5328}(601, \cdot)\) None 0 6
5328.2.ib \(\chi_{5328}(599, \cdot)\) None 0 6
5328.2.if \(\chi_{5328}(719, \cdot)\) n/a 456 6
5328.2.ii \(\chi_{5328}(527, \cdot)\) n/a 1368 6
5328.2.ij \(\chi_{5328}(95, \cdot)\) n/a 1368 6
5328.2.im \(\chi_{5328}(287, \cdot)\) n/a 456 6
5328.2.in \(\chi_{5328}(289, \cdot)\) n/a 564 6
5328.2.iq \(\chi_{5328}(817, \cdot)\) n/a 1356 6
5328.2.is \(\chi_{5328}(71, \cdot)\) None 0 6
5328.2.it \(\chi_{5328}(551, \cdot)\) None 0 6
5328.2.iw \(\chi_{5328}(1033, \cdot)\) None 0 6
5328.2.ix \(\chi_{5328}(793, \cdot)\) None 0 6
5328.2.ja \(\chi_{5328}(361, \cdot)\) None 0 6
5328.2.jb \(\chi_{5328}(1177, \cdot)\) None 0 6
5328.2.je \(\chi_{5328}(263, \cdot)\) None 0 6
5328.2.jf \(\chi_{5328}(215, \cdot)\) None 0 6
5328.2.ji \(\chi_{5328}(337, \cdot)\) n/a 1356 6
5328.2.jj \(\chi_{5328}(1103, \cdot)\) n/a 1368 6
5328.2.jm \(\chi_{5328}(959, \cdot)\) n/a 1368 6
5328.2.jq \(\chi_{5328}(679, \cdot)\) None 0 12
5328.2.jr \(\chi_{5328}(281, \cdot)\) None 0 12
5328.2.js \(\chi_{5328}(79, \cdot)\) n/a 2736 12
5328.2.jt \(\chi_{5328}(113, \cdot)\) n/a 2712 12
5328.2.jw \(\chi_{5328}(17, \cdot)\) n/a 912 12
5328.2.jx \(\chi_{5328}(1423, \cdot)\) n/a 1140 12
5328.2.ka \(\chi_{5328}(229, \cdot)\) n/a 10896 12
5328.2.kc \(\chi_{5328}(83, \cdot)\) n/a 10896 12
5328.2.ke \(\chi_{5328}(469, \cdot)\) n/a 4536 12
5328.2.kh \(\chi_{5328}(299, \cdot)\) n/a 10896 12
5328.2.kj \(\chi_{5328}(781, \cdot)\) n/a 10896 12
5328.2.kk \(\chi_{5328}(395, \cdot)\) n/a 3648 12
5328.2.km \(\chi_{5328}(331, \cdot)\) n/a 10896 12
5328.2.kn \(\chi_{5328}(461, \cdot)\) n/a 10896 12
5328.2.kq \(\chi_{5328}(557, \cdot)\) n/a 3648 12
5328.2.kr \(\chi_{5328}(19, \cdot)\) n/a 4536 12
5328.2.ku \(\chi_{5328}(389, \cdot)\) n/a 10896 12
5328.2.kv \(\chi_{5328}(355, \cdot)\) n/a 10896 12
5328.2.la \(\chi_{5328}(605, \cdot)\) n/a 10896 12
5328.2.lb \(\chi_{5328}(907, \cdot)\) n/a 10896 12
5328.2.le \(\chi_{5328}(701, \cdot)\) n/a 3648 12
5328.2.lf \(\chi_{5328}(91, \cdot)\) n/a 4536 12
5328.2.li \(\chi_{5328}(187, \cdot)\) n/a 10896 12
5328.2.lj \(\chi_{5328}(5, \cdot)\) n/a 10896 12
5328.2.lk \(\chi_{5328}(107, \cdot)\) n/a 3648 12
5328.2.ln \(\chi_{5328}(157, \cdot)\) n/a 10896 12
5328.2.lp \(\chi_{5328}(155, \cdot)\) n/a 10896 12
5328.2.lq \(\chi_{5328}(181, \cdot)\) n/a 4536 12
5328.2.ls \(\chi_{5328}(707, \cdot)\) n/a 10896 12
5328.2.lu \(\chi_{5328}(373, \cdot)\) n/a 10896 12
5328.2.lw \(\chi_{5328}(425, \cdot)\) None 0 12
5328.2.lx \(\chi_{5328}(439, \cdot)\) None 0 12
5328.2.ma \(\chi_{5328}(55, \cdot)\) None 0 12
5328.2.mb \(\chi_{5328}(89, \cdot)\) None 0 12
5328.2.mg \(\chi_{5328}(353, \cdot)\) n/a 2712 12
5328.2.mh \(\chi_{5328}(463, \cdot)\) n/a 2736 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5328))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5328)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1332))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1776))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2664))\)\(^{\oplus 2}\)