Properties

Label 6864.2
Level 6864
Weight 2
Dimension 527096
Nonzero newspaces 112
Sturm bound 5160960

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Defining parameters

Level: \( N \) = \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 112 \)
Sturm bound: \(5160960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6864))\).

Total New Old
Modular forms 1303680 530656 773024
Cusp forms 1276801 527096 749705
Eisenstein series 26879 3560 23319

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6864))\)

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
6864.2.a \(\chi_{6864}(1, \cdot)\) 6864.2.a.a 1 1
6864.2.a.b 1
6864.2.a.c 1
6864.2.a.d 1
6864.2.a.e 1
6864.2.a.f 1
6864.2.a.g 1
6864.2.a.h 1
6864.2.a.i 1
6864.2.a.j 1
6864.2.a.k 1
6864.2.a.l 1
6864.2.a.m 1
6864.2.a.n 1
6864.2.a.o 1
6864.2.a.p 1
6864.2.a.q 1
6864.2.a.r 1
6864.2.a.s 1
6864.2.a.t 1
6864.2.a.u 1
6864.2.a.v 1
6864.2.a.w 1
6864.2.a.x 1
6864.2.a.y 1
6864.2.a.z 1
6864.2.a.ba 1
6864.2.a.bb 2
6864.2.a.bc 2
6864.2.a.bd 2
6864.2.a.be 2
6864.2.a.bf 2
6864.2.a.bg 2
6864.2.a.bh 2
6864.2.a.bi 2
6864.2.a.bj 2
6864.2.a.bk 2
6864.2.a.bl 2
6864.2.a.bm 2
6864.2.a.bn 3
6864.2.a.bo 3
6864.2.a.bp 3
6864.2.a.bq 3
6864.2.a.br 3
6864.2.a.bs 3
6864.2.a.bt 3
6864.2.a.bu 3
6864.2.a.bv 3
6864.2.a.bw 4
6864.2.a.bx 4
6864.2.a.by 4
6864.2.a.bz 4
6864.2.a.ca 4
6864.2.a.cb 4
6864.2.a.cc 4
6864.2.a.cd 4
6864.2.a.ce 5
6864.2.a.cf 5
6864.2.b \(\chi_{6864}(2287, \cdot)\) n/a 168 1
6864.2.c \(\chi_{6864}(287, \cdot)\) n/a 240 1
6864.2.f \(\chi_{6864}(2705, \cdot)\) n/a 288 1
6864.2.g \(\chi_{6864}(1585, \cdot)\) n/a 140 1
6864.2.j \(\chi_{6864}(4135, \cdot)\) None 0 1
6864.2.k \(\chi_{6864}(5303, \cdot)\) None 0 1
6864.2.n \(\chi_{6864}(857, \cdot)\) None 0 1
6864.2.o \(\chi_{6864}(3433, \cdot)\) None 0 1
6864.2.t \(\chi_{6864}(5719, \cdot)\) None 0 1
6864.2.u \(\chi_{6864}(3719, \cdot)\) None 0 1
6864.2.x \(\chi_{6864}(6137, \cdot)\) None 0 1
6864.2.y \(\chi_{6864}(5017, \cdot)\) None 0 1
6864.2.bb \(\chi_{6864}(703, \cdot)\) n/a 144 1
6864.2.bc \(\chi_{6864}(1871, \cdot)\) n/a 280 1
6864.2.bf \(\chi_{6864}(4289, \cdot)\) n/a 332 1
6864.2.bg \(\chi_{6864}(529, \cdot)\) n/a 280 2
6864.2.bh \(\chi_{6864}(1123, \cdot)\) n/a 1120 2
6864.2.bi \(\chi_{6864}(395, \cdot)\) n/a 2672 2
6864.2.bl \(\chi_{6864}(749, \cdot)\) n/a 2240 2
6864.2.bm \(\chi_{6864}(109, \cdot)\) n/a 1344 2
6864.2.bq \(\chi_{6864}(155, \cdot)\) n/a 2240 2
6864.2.br \(\chi_{6864}(2419, \cdot)\) n/a 1152 2
6864.2.bu \(\chi_{6864}(1717, \cdot)\) n/a 960 2
6864.2.bv \(\chi_{6864}(2573, \cdot)\) n/a 2672 2
6864.2.by \(\chi_{6864}(5543, \cdot)\) None 0 2
6864.2.bz \(\chi_{6864}(2111, \cdot)\) n/a 672 2
6864.2.cc \(\chi_{6864}(2839, \cdot)\) None 0 2
6864.2.cd \(\chi_{6864}(463, \cdot)\) n/a 280 2
6864.2.cf \(\chi_{6864}(1825, \cdot)\) n/a 336 2
6864.2.ci \(\chi_{6864}(5257, \cdot)\) None 0 2
6864.2.cj \(\chi_{6864}(1409, \cdot)\) n/a 560 2
6864.2.cm \(\chi_{6864}(4841, \cdot)\) None 0 2
6864.2.cn \(\chi_{6864}(2003, \cdot)\) n/a 1920 2
6864.2.cq \(\chi_{6864}(571, \cdot)\) n/a 1344 2
6864.2.cr \(\chi_{6864}(3301, \cdot)\) n/a 1120 2
6864.2.cu \(\chi_{6864}(989, \cdot)\) n/a 2304 2
6864.2.cx \(\chi_{6864}(2179, \cdot)\) n/a 1120 2
6864.2.cy \(\chi_{6864}(1451, \cdot)\) n/a 2672 2
6864.2.db \(\chi_{6864}(4181, \cdot)\) n/a 2240 2
6864.2.dc \(\chi_{6864}(1165, \cdot)\) n/a 1344 2
6864.2.dd \(\chi_{6864}(625, \cdot)\) n/a 576 4
6864.2.dg \(\chi_{6864}(1849, \cdot)\) None 0 2
6864.2.dh \(\chi_{6864}(329, \cdot)\) None 0 2
6864.2.dk \(\chi_{6864}(23, \cdot)\) None 0 2
6864.2.dl \(\chi_{6864}(2551, \cdot)\) None 0 2
6864.2.do \(\chi_{6864}(1057, \cdot)\) n/a 280 2
6864.2.dp \(\chi_{6864}(1121, \cdot)\) n/a 664 2
6864.2.ds \(\chi_{6864}(815, \cdot)\) n/a 560 2
6864.2.dt \(\chi_{6864}(1759, \cdot)\) n/a 336 2
6864.2.du \(\chi_{6864}(3761, \cdot)\) n/a 664 2
6864.2.dx \(\chi_{6864}(1343, \cdot)\) n/a 560 2
6864.2.dy \(\chi_{6864}(1231, \cdot)\) n/a 336 2
6864.2.eb \(\chi_{6864}(4489, \cdot)\) None 0 2
6864.2.ec \(\chi_{6864}(4553, \cdot)\) None 0 2
6864.2.ef \(\chi_{6864}(2135, \cdot)\) None 0 2
6864.2.eg \(\chi_{6864}(439, \cdot)\) None 0 2
6864.2.ej \(\chi_{6864}(545, \cdot)\) n/a 1328 4
6864.2.em \(\chi_{6864}(79, \cdot)\) n/a 576 4
6864.2.en \(\chi_{6864}(1247, \cdot)\) n/a 1344 4
6864.2.eq \(\chi_{6864}(2393, \cdot)\) None 0 4
6864.2.er \(\chi_{6864}(25, \cdot)\) None 0 4
6864.2.eu \(\chi_{6864}(1975, \cdot)\) None 0 4
6864.2.ev \(\chi_{6864}(599, \cdot)\) None 0 4
6864.2.fa \(\chi_{6864}(233, \cdot)\) None 0 4
6864.2.fb \(\chi_{6864}(313, \cdot)\) None 0 4
6864.2.fe \(\chi_{6864}(391, \cdot)\) None 0 4
6864.2.ff \(\chi_{6864}(311, \cdot)\) None 0 4
6864.2.fi \(\chi_{6864}(833, \cdot)\) n/a 1152 4
6864.2.fj \(\chi_{6864}(961, \cdot)\) n/a 672 4
6864.2.fm \(\chi_{6864}(415, \cdot)\) n/a 672 4
6864.2.fn \(\chi_{6864}(911, \cdot)\) n/a 1152 4
6864.2.fq \(\chi_{6864}(1957, \cdot)\) n/a 2688 4
6864.2.fr \(\chi_{6864}(1805, \cdot)\) n/a 4480 4
6864.2.fu \(\chi_{6864}(2243, \cdot)\) n/a 5344 4
6864.2.fv \(\chi_{6864}(67, \cdot)\) n/a 2240 4
6864.2.fx \(\chi_{6864}(1517, \cdot)\) n/a 5344 4
6864.2.fy \(\chi_{6864}(1453, \cdot)\) n/a 2240 4
6864.2.gb \(\chi_{6864}(43, \cdot)\) n/a 2688 4
6864.2.gc \(\chi_{6864}(419, \cdot)\) n/a 4480 4
6864.2.ge \(\chi_{6864}(89, \cdot)\) None 0 4
6864.2.gh \(\chi_{6864}(353, \cdot)\) n/a 1120 4
6864.2.gi \(\chi_{6864}(505, \cdot)\) None 0 4
6864.2.gl \(\chi_{6864}(241, \cdot)\) n/a 672 4
6864.2.gn \(\chi_{6864}(1519, \cdot)\) n/a 560 4
6864.2.go \(\chi_{6864}(1255, \cdot)\) None 0 4
6864.2.gr \(\chi_{6864}(527, \cdot)\) n/a 1344 4
6864.2.gs \(\chi_{6864}(791, \cdot)\) None 0 4
6864.2.gu \(\chi_{6864}(725, \cdot)\) n/a 5344 4
6864.2.gx \(\chi_{6864}(133, \cdot)\) n/a 2240 4
6864.2.gy \(\chi_{6864}(835, \cdot)\) n/a 2688 4
6864.2.hb \(\chi_{6864}(1739, \cdot)\) n/a 4480 4
6864.2.hc \(\chi_{6864}(2221, \cdot)\) n/a 2688 4
6864.2.hd \(\chi_{6864}(1541, \cdot)\) n/a 4480 4
6864.2.hg \(\chi_{6864}(2507, \cdot)\) n/a 5344 4
6864.2.hh \(\chi_{6864}(331, \cdot)\) n/a 2240 4
6864.2.hk \(\chi_{6864}(289, \cdot)\) n/a 1344 8
6864.2.hl \(\chi_{6864}(317, \cdot)\) n/a 10688 8
6864.2.hm \(\chi_{6864}(541, \cdot)\) n/a 5376 8
6864.2.hp \(\chi_{6864}(1435, \cdot)\) n/a 5376 8
6864.2.hq \(\chi_{6864}(83, \cdot)\) n/a 10688 8
6864.2.hu \(\chi_{6864}(181, \cdot)\) n/a 5376 8
6864.2.hv \(\chi_{6864}(365, \cdot)\) n/a 9216 8
6864.2.hy \(\chi_{6864}(443, \cdot)\) n/a 9216 8
6864.2.hz \(\chi_{6864}(259, \cdot)\) n/a 5376 8
6864.2.ib \(\chi_{6864}(73, \cdot)\) None 0 8
6864.2.ie \(\chi_{6864}(1009, \cdot)\) n/a 1344 8
6864.2.if \(\chi_{6864}(905, \cdot)\) None 0 8
6864.2.ii \(\chi_{6864}(785, \cdot)\) n/a 2656 8
6864.2.ik \(\chi_{6864}(239, \cdot)\) n/a 2688 8
6864.2.il \(\chi_{6864}(359, \cdot)\) None 0 8
6864.2.io \(\chi_{6864}(31, \cdot)\) n/a 1344 8
6864.2.ip \(\chi_{6864}(775, \cdot)\) None 0 8
6864.2.ir \(\chi_{6864}(157, \cdot)\) n/a 4608 8
6864.2.iu \(\chi_{6864}(701, \cdot)\) n/a 10688 8
6864.2.iv \(\chi_{6864}(467, \cdot)\) n/a 10688 8
6864.2.iy \(\chi_{6864}(547, \cdot)\) n/a 4608 8
6864.2.jb \(\chi_{6864}(5, \cdot)\) n/a 10688 8
6864.2.jc \(\chi_{6864}(733, \cdot)\) n/a 5376 8
6864.2.jf \(\chi_{6864}(499, \cdot)\) n/a 5376 8
6864.2.jg \(\chi_{6864}(1019, \cdot)\) n/a 10688 8
6864.2.jj \(\chi_{6864}(1127, \cdot)\) None 0 8
6864.2.jk \(\chi_{6864}(1063, \cdot)\) None 0 8
6864.2.jn \(\chi_{6864}(361, \cdot)\) None 0 8
6864.2.jo \(\chi_{6864}(425, \cdot)\) None 0 8
6864.2.jr \(\chi_{6864}(335, \cdot)\) n/a 2688 8
6864.2.js \(\chi_{6864}(607, \cdot)\) n/a 1344 8
6864.2.jv \(\chi_{6864}(17, \cdot)\) n/a 2656 8
6864.2.jw \(\chi_{6864}(191, \cdot)\) n/a 2688 8
6864.2.jx \(\chi_{6864}(127, \cdot)\) n/a 1344 8
6864.2.ka \(\chi_{6864}(49, \cdot)\) n/a 1344 8
6864.2.kb \(\chi_{6864}(497, \cdot)\) n/a 2656 8
6864.2.ke \(\chi_{6864}(647, \cdot)\) None 0 8
6864.2.kf \(\chi_{6864}(679, \cdot)\) None 0 8
6864.2.ki \(\chi_{6864}(841, \cdot)\) None 0 8
6864.2.kj \(\chi_{6864}(569, \cdot)\) None 0 8
6864.2.ko \(\chi_{6864}(227, \cdot)\) n/a 21376 16
6864.2.kp \(\chi_{6864}(115, \cdot)\) n/a 10752 16
6864.2.ks \(\chi_{6864}(349, \cdot)\) n/a 10752 16
6864.2.kt \(\chi_{6864}(245, \cdot)\) n/a 21376 16
6864.2.kv \(\chi_{6864}(139, \cdot)\) n/a 10752 16
6864.2.kw \(\chi_{6864}(179, \cdot)\) n/a 21376 16
6864.2.kz \(\chi_{6864}(101, \cdot)\) n/a 21376 16
6864.2.la \(\chi_{6864}(445, \cdot)\) n/a 10752 16
6864.2.ld \(\chi_{6864}(487, \cdot)\) None 0 16
6864.2.le \(\chi_{6864}(223, \cdot)\) n/a 2688 16
6864.2.lh \(\chi_{6864}(167, \cdot)\) None 0 16
6864.2.li \(\chi_{6864}(431, \cdot)\) n/a 5376 16
6864.2.lk \(\chi_{6864}(401, \cdot)\) n/a 5312 16
6864.2.ln \(\chi_{6864}(137, \cdot)\) None 0 16
6864.2.lo \(\chi_{6864}(145, \cdot)\) n/a 2688 16
6864.2.lr \(\chi_{6864}(409, \cdot)\) None 0 16
6864.2.ls \(\chi_{6864}(283, \cdot)\) n/a 10752 16
6864.2.lv \(\chi_{6864}(731, \cdot)\) n/a 21376 16
6864.2.lw \(\chi_{6864}(29, \cdot)\) n/a 21376 16
6864.2.lz \(\chi_{6864}(829, \cdot)\) n/a 10752 16
6864.2.ma \(\chi_{6864}(371, \cdot)\) n/a 21376 16
6864.2.mb \(\chi_{6864}(427, \cdot)\) n/a 10752 16
6864.2.me \(\chi_{6864}(85, \cdot)\) n/a 10752 16
6864.2.mf \(\chi_{6864}(773, \cdot)\) n/a 21376 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6864))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6864)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1716))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3432))\)\(^{\oplus 2}\)