# Properties

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

## 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

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