# Properties

 Label 6825.2 Level 6825 Weight 2 Dimension 1051172 Nonzero newspaces 200 Sturm bound 6451200

## Defining parameters

 Level: $$N$$ = $$6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$200$$ Sturm bound: $$6451200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6825))$$.

Total New Old
Modular forms 1628928 1060188 568740
Cusp forms 1596673 1051172 545501
Eisenstein series 32255 9016 23239

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6825))$$

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
6825.2.a $$\chi_{6825}(1, \cdot)$$ 6825.2.a.a 1 1
6825.2.a.b 1
6825.2.a.c 1
6825.2.a.d 1
6825.2.a.e 1
6825.2.a.f 1
6825.2.a.g 1
6825.2.a.h 1
6825.2.a.i 1
6825.2.a.j 1
6825.2.a.k 1
6825.2.a.l 1
6825.2.a.m 2
6825.2.a.n 2
6825.2.a.o 2
6825.2.a.p 2
6825.2.a.q 2
6825.2.a.r 2
6825.2.a.s 2
6825.2.a.t 2
6825.2.a.u 2
6825.2.a.v 2
6825.2.a.w 2
6825.2.a.x 3
6825.2.a.y 3
6825.2.a.z 3
6825.2.a.ba 3
6825.2.a.bb 3
6825.2.a.bc 3
6825.2.a.bd 3
6825.2.a.be 4
6825.2.a.bf 4
6825.2.a.bg 4
6825.2.a.bh 4
6825.2.a.bi 4
6825.2.a.bj 4
6825.2.a.bk 4
6825.2.a.bl 4
6825.2.a.bm 4
6825.2.a.bn 4
6825.2.a.bo 5
6825.2.a.bp 6
6825.2.a.bq 6
6825.2.a.br 6
6825.2.a.bs 6
6825.2.a.bt 6
6825.2.a.bu 6
6825.2.a.bv 8
6825.2.a.bw 8
6825.2.a.bx 8
6825.2.a.by 8
6825.2.a.bz 8
6825.2.a.ca 8
6825.2.a.cb 10
6825.2.a.cc 10
6825.2.a.cd 12
6825.2.a.ce 12
6825.2.d $$\chi_{6825}(1301, \cdot)$$ n/a 608 1
6825.2.e $$\chi_{6825}(5251, \cdot)$$ n/a 264 1
6825.2.f $$\chi_{6825}(274, \cdot)$$ n/a 216 1
6825.2.g $$\chi_{6825}(6824, \cdot)$$ n/a 664 1
6825.2.j $$\chi_{6825}(5524, \cdot)$$ n/a 256 1
6825.2.k $$\chi_{6825}(1574, \cdot)$$ n/a 576 1
6825.2.p $$\chi_{6825}(6551, \cdot)$$ n/a 696 1
6825.2.q $$\chi_{6825}(1576, \cdot)$$ n/a 536 2
6825.2.r $$\chi_{6825}(3901, \cdot)$$ n/a 608 2
6825.2.s $$\chi_{6825}(3376, \cdot)$$ n/a 710 2
6825.2.t $$\chi_{6825}(4351, \cdot)$$ n/a 710 2
6825.2.v $$\chi_{6825}(1282, \cdot)$$ n/a 504 2
6825.2.w $$\chi_{6825}(3632, \cdot)$$ n/a 1328 2
6825.2.y $$\chi_{6825}(3457, \cdot)$$ n/a 672 2
6825.2.z $$\chi_{6825}(1457, \cdot)$$ n/a 864 2
6825.2.bc $$\chi_{6825}(4649, \cdot)$$ n/a 1008 2
6825.2.bd $$\chi_{6825}(1399, \cdot)$$ n/a 672 2
6825.2.bi $$\chi_{6825}(1126, \cdot)$$ n/a 712 2
6825.2.bj $$\chi_{6825}(4376, \cdot)$$ n/a 1064 2
6825.2.bm $$\chi_{6825}(118, \cdot)$$ n/a 576 2
6825.2.bn $$\chi_{6825}(1793, \cdot)$$ n/a 1008 2
6825.2.bo $$\chi_{6825}(2332, \cdot)$$ n/a 504 2
6825.2.br $$\chi_{6825}(2582, \cdot)$$ n/a 1328 2
6825.2.bs $$\chi_{6825}(1366, \cdot)$$ n/a 1440 4
6825.2.bt $$\chi_{6825}(4624, \cdot)$$ n/a 672 2
6825.2.bu $$\chi_{6825}(1349, \cdot)$$ n/a 1328 2
6825.2.bz $$\chi_{6825}(2726, \cdot)$$ n/a 1394 2
6825.2.ca $$\chi_{6825}(751, \cdot)$$ n/a 710 2
6825.2.cd $$\chi_{6825}(3974, \cdot)$$ n/a 1328 2
6825.2.ce $$\chi_{6825}(1999, \cdot)$$ n/a 672 2
6825.2.cf $$\chi_{6825}(251, \cdot)$$ n/a 1396 2
6825.2.cg $$\chi_{6825}(1676, \cdot)$$ n/a 1396 2
6825.2.cp $$\chi_{6825}(3524, \cdot)$$ n/a 1152 2
6825.2.cq $$\chi_{6825}(2599, \cdot)$$ n/a 672 2
6825.2.cr $$\chi_{6825}(1049, \cdot)$$ n/a 1328 2
6825.2.cs $$\chi_{6825}(3949, \cdot)$$ n/a 512 2
6825.2.ct $$\chi_{6825}(101, \cdot)$$ n/a 1394 2
6825.2.cw $$\chi_{6825}(1726, \cdot)$$ n/a 710 2
6825.2.cx $$\chi_{6825}(3701, \cdot)$$ n/a 1394 2
6825.2.de $$\chi_{6825}(1949, \cdot)$$ n/a 1328 2
6825.2.df $$\chi_{6825}(4174, \cdot)$$ n/a 576 2
6825.2.dg $$\chi_{6825}(524, \cdot)$$ n/a 1328 2
6825.2.dh $$\chi_{6825}(1849, \cdot)$$ n/a 496 2
6825.2.di $$\chi_{6825}(3676, \cdot)$$ n/a 528 2
6825.2.dj $$\chi_{6825}(776, \cdot)$$ n/a 1396 2
6825.2.dk $$\chi_{6825}(2326, \cdot)$$ n/a 708 2
6825.2.dl $$\chi_{6825}(3251, \cdot)$$ n/a 1216 2
6825.2.ds $$\chi_{6825}(374, \cdot)$$ n/a 1328 2
6825.2.dt $$\chi_{6825}(3649, \cdot)$$ n/a 672 2
6825.2.dw $$\chi_{6825}(1076, \cdot)$$ n/a 1394 2
6825.2.dx $$\chi_{6825}(1024, \cdot)$$ n/a 672 2
6825.2.dy $$\chi_{6825}(2999, \cdot)$$ n/a 1328 2
6825.2.eb $$\chi_{6825}(1091, \cdot)$$ n/a 4448 4
6825.2.eg $$\chi_{6825}(209, \cdot)$$ n/a 3840 4
6825.2.eh $$\chi_{6825}(64, \cdot)$$ n/a 1664 4
6825.2.ek $$\chi_{6825}(1364, \cdot)$$ n/a 4448 4
6825.2.el $$\chi_{6825}(1639, \cdot)$$ n/a 1440 4
6825.2.em $$\chi_{6825}(1156, \cdot)$$ n/a 1696 4
6825.2.en $$\chi_{6825}(2666, \cdot)$$ n/a 3840 4
6825.2.er $$\chi_{6825}(782, \cdot)$$ n/a 2656 4
6825.2.es $$\chi_{6825}(1957, \cdot)$$ n/a 1344 4
6825.2.ev $$\chi_{6825}(268, \cdot)$$ n/a 1344 4
6825.2.ex $$\chi_{6825}(1307, \cdot)$$ n/a 2656 4
6825.2.ez $$\chi_{6825}(1532, \cdot)$$ n/a 2656 4
6825.2.fa $$\chi_{6825}(2143, \cdot)$$ n/a 1008 4
6825.2.fc $$\chi_{6825}(193, \cdot)$$ n/a 1344 4
6825.2.fe $$\chi_{6825}(668, \cdot)$$ n/a 2656 4
6825.2.fg $$\chi_{6825}(368, \cdot)$$ n/a 2656 4
6825.2.fh $$\chi_{6825}(1543, \cdot)$$ n/a 1344 4
6825.2.fm $$\chi_{6825}(674, \cdot)$$ n/a 2656 4
6825.2.fn $$\chi_{6825}(1774, \cdot)$$ n/a 1344 4
6825.2.fo $$\chi_{6825}(1501, \cdot)$$ n/a 1420 4
6825.2.fp $$\chi_{6825}(401, \cdot)$$ n/a 2788 4
6825.2.fu $$\chi_{6825}(107, \cdot)$$ n/a 2656 4
6825.2.fv $$\chi_{6825}(1018, \cdot)$$ n/a 1344 4
6825.2.fw $$\chi_{6825}(1082, \cdot)$$ n/a 2656 4
6825.2.fx $$\chi_{6825}(82, \cdot)$$ n/a 1344 4
6825.2.ga $$\chi_{6825}(157, \cdot)$$ n/a 1152 4
6825.2.gb $$\chi_{6825}(218, \cdot)$$ n/a 2016 4
6825.2.gc $$\chi_{6825}(1693, \cdot)$$ n/a 1344 4
6825.2.gd $$\chi_{6825}(3782, \cdot)$$ n/a 2656 4
6825.2.gk $$\chi_{6825}(1376, \cdot)$$ n/a 2788 4
6825.2.gl $$\chi_{6825}(176, \cdot)$$ n/a 2128 4
6825.2.gm $$\chi_{6825}(2026, \cdot)$$ n/a 1420 4
6825.2.gn $$\chi_{6825}(76, \cdot)$$ n/a 1416 4
6825.2.gs $$\chi_{6825}(1451, \cdot)$$ n/a 2792 4
6825.2.gt $$\chi_{6825}(3076, \cdot)$$ n/a 1416 4
6825.2.gu $$\chi_{6825}(3349, \cdot)$$ n/a 1344 4
6825.2.gv $$\chi_{6825}(1724, \cdot)$$ n/a 2656 4
6825.2.ha $$\chi_{6825}(349, \cdot)$$ n/a 1344 4
6825.2.hb $$\chi_{6825}(124, \cdot)$$ n/a 1344 4
6825.2.hc $$\chi_{6825}(449, \cdot)$$ n/a 2016 4
6825.2.hd $$\chi_{6825}(149, \cdot)$$ n/a 2656 4
6825.2.hk $$\chi_{6825}(493, \cdot)$$ n/a 1344 4
6825.2.hl $$\chi_{6825}(932, \cdot)$$ n/a 2016 4
6825.2.hm $$\chi_{6825}(1882, \cdot)$$ n/a 1344 4
6825.2.hn $$\chi_{6825}(443, \cdot)$$ n/a 2304 4
6825.2.hq $$\chi_{6825}(3182, \cdot)$$ n/a 2656 4
6825.2.hr $$\chi_{6825}(607, \cdot)$$ n/a 1344 4
6825.2.hs $$\chi_{6825}(1318, \cdot)$$ n/a 1344 4
6825.2.hu $$\chi_{6825}(293, \cdot)$$ n/a 2656 4
6825.2.hw $$\chi_{6825}(3218, \cdot)$$ n/a 2656 4
6825.2.hz $$\chi_{6825}(982, \cdot)$$ n/a 1344 4
6825.2.ib $$\chi_{6825}(232, \cdot)$$ n/a 1008 4
6825.2.id $$\chi_{6825}(593, \cdot)$$ n/a 2656 4
6825.2.ie $$\chi_{6825}(332, \cdot)$$ n/a 2656 4
6825.2.ih $$\chi_{6825}(457, \cdot)$$ n/a 1344 4
6825.2.ii $$\chi_{6825}(16, \cdot)$$ n/a 4480 8
6825.2.ij $$\chi_{6825}(646, \cdot)$$ n/a 4480 8
6825.2.ik $$\chi_{6825}(781, \cdot)$$ n/a 3840 8
6825.2.il $$\chi_{6825}(211, \cdot)$$ n/a 3328 8
6825.2.im $$\chi_{6825}(83, \cdot)$$ n/a 8896 8
6825.2.ip $$\chi_{6825}(463, \cdot)$$ n/a 3360 8
6825.2.iq $$\chi_{6825}(428, \cdot)$$ n/a 6720 8
6825.2.ir $$\chi_{6825}(937, \cdot)$$ n/a 3840 8
6825.2.iu $$\chi_{6825}(281, \cdot)$$ n/a 6720 8
6825.2.iv $$\chi_{6825}(811, \cdot)$$ n/a 4480 8
6825.2.ja $$\chi_{6825}(34, \cdot)$$ n/a 4480 8
6825.2.jb $$\chi_{6825}(239, \cdot)$$ n/a 6720 8
6825.2.je $$\chi_{6825}(92, \cdot)$$ n/a 5760 8
6825.2.jf $$\chi_{6825}(727, \cdot)$$ n/a 4480 8
6825.2.jh $$\chi_{6825}(398, \cdot)$$ n/a 8896 8
6825.2.ji $$\chi_{6825}(148, \cdot)$$ n/a 3360 8
6825.2.jm $$\chi_{6825}(269, \cdot)$$ n/a 8896 8
6825.2.jn $$\chi_{6825}(4, \cdot)$$ n/a 4480 8
6825.2.jo $$\chi_{6825}(836, \cdot)$$ n/a 8896 8
6825.2.jr $$\chi_{6825}(919, \cdot)$$ n/a 4480 8
6825.2.js $$\chi_{6825}(719, \cdot)$$ n/a 8896 8
6825.2.jz $$\chi_{6825}(131, \cdot)$$ n/a 7680 8
6825.2.ka $$\chi_{6825}(571, \cdot)$$ n/a 4480 8
6825.2.kb $$\chi_{6825}(146, \cdot)$$ n/a 8896 8
6825.2.kc $$\chi_{6825}(316, \cdot)$$ n/a 3392 8
6825.2.kd $$\chi_{6825}(484, \cdot)$$ n/a 3392 8
6825.2.ke $$\chi_{6825}(1154, \cdot)$$ n/a 8896 8
6825.2.kf $$\chi_{6825}(79, \cdot)$$ n/a 3840 8
6825.2.kg $$\chi_{6825}(194, \cdot)$$ n/a 8896 8
6825.2.kn $$\chi_{6825}(731, \cdot)$$ n/a 8896 8
6825.2.ko $$\chi_{6825}(121, \cdot)$$ n/a 4480 8
6825.2.kr $$\chi_{6825}(446, \cdot)$$ n/a 8896 8
6825.2.ks $$\chi_{6825}(589, \cdot)$$ n/a 3328 8
6825.2.kt $$\chi_{6825}(419, \cdot)$$ n/a 8896 8
6825.2.ku $$\chi_{6825}(844, \cdot)$$ n/a 4480 8
6825.2.kv $$\chi_{6825}(404, \cdot)$$ n/a 7680 8
6825.2.le $$\chi_{6825}(311, \cdot)$$ n/a 8896 8
6825.2.lf $$\chi_{6825}(881, \cdot)$$ n/a 8896 8
6825.2.lg $$\chi_{6825}(394, \cdot)$$ n/a 4480 8
6825.2.lh $$\chi_{6825}(1004, \cdot)$$ n/a 8896 8
6825.2.lk $$\chi_{6825}(1096, \cdot)$$ n/a 4480 8
6825.2.ll $$\chi_{6825}(341, \cdot)$$ n/a 8896 8
6825.2.lq $$\chi_{6825}(1109, \cdot)$$ n/a 8896 8
6825.2.lr $$\chi_{6825}(289, \cdot)$$ n/a 4480 8
6825.2.ls $$\chi_{6825}(487, \cdot)$$ n/a 8960 16
6825.2.lv $$\chi_{6825}(362, \cdot)$$ n/a 17792 16
6825.2.lw $$\chi_{6825}(122, \cdot)$$ n/a 17792 16
6825.2.ly $$\chi_{6825}(253, \cdot)$$ n/a 6720 16
6825.2.ma $$\chi_{6825}(58, \cdot)$$ n/a 8960 16
6825.2.md $$\chi_{6825}(488, \cdot)$$ n/a 17792 16
6825.2.mf $$\chi_{6825}(587, \cdot)$$ n/a 17792 16
6825.2.mh $$\chi_{6825}(697, \cdot)$$ n/a 8960 16
6825.2.mi $$\chi_{6825}(367, \cdot)$$ n/a 8960 16
6825.2.mj $$\chi_{6825}(212, \cdot)$$ n/a 17792 16
6825.2.mm $$\chi_{6825}(53, \cdot)$$ n/a 15360 16
6825.2.mn $$\chi_{6825}(433, \cdot)$$ n/a 8960 16
6825.2.mo $$\chi_{6825}(113, \cdot)$$ n/a 13440 16
6825.2.mp $$\chi_{6825}(103, \cdot)$$ n/a 8960 16
6825.2.mw $$\chi_{6825}(254, \cdot)$$ n/a 17792 16
6825.2.mx $$\chi_{6825}(344, \cdot)$$ n/a 13440 16
6825.2.my $$\chi_{6825}(19, \cdot)$$ n/a 8960 16
6825.2.mz $$\chi_{6825}(769, \cdot)$$ n/a 8960 16
6825.2.ne $$\chi_{6825}(44, \cdot)$$ n/a 17792 16
6825.2.nf $$\chi_{6825}(229, \cdot)$$ n/a 8960 16
6825.2.ng $$\chi_{6825}(31, \cdot)$$ n/a 8960 16
6825.2.nh $$\chi_{6825}(86, \cdot)$$ n/a 17792 16
6825.2.nm $$\chi_{6825}(496, \cdot)$$ n/a 8960 16
6825.2.nn $$\chi_{6825}(661, \cdot)$$ n/a 8960 16
6825.2.no $$\chi_{6825}(71, \cdot)$$ n/a 13440 16
6825.2.np $$\chi_{6825}(11, \cdot)$$ n/a 17792 16
6825.2.nw $$\chi_{6825}(233, \cdot)$$ n/a 17792 16
6825.2.nx $$\chi_{6825}(328, \cdot)$$ n/a 8960 16
6825.2.ny $$\chi_{6825}(953, \cdot)$$ n/a 13440 16
6825.2.nz $$\chi_{6825}(313, \cdot)$$ n/a 7680 16
6825.2.oc $$\chi_{6825}(283, \cdot)$$ n/a 8960 16
6825.2.od $$\chi_{6825}(263, \cdot)$$ n/a 17792 16
6825.2.oe $$\chi_{6825}(472, \cdot)$$ n/a 8960 16
6825.2.of $$\chi_{6825}(347, \cdot)$$ n/a 17792 16
6825.2.ok $$\chi_{6825}(821, \cdot)$$ n/a 17792 16
6825.2.ol $$\chi_{6825}(136, \cdot)$$ n/a 8960 16
6825.2.om $$\chi_{6825}(409, \cdot)$$ n/a 8960 16
6825.2.on $$\chi_{6825}(1094, \cdot)$$ n/a 17792 16
6825.2.os $$\chi_{6825}(178, \cdot)$$ n/a 8960 16
6825.2.ot $$\chi_{6825}(23, \cdot)$$ n/a 17792 16
6825.2.ov $$\chi_{6825}(47, \cdot)$$ n/a 17792 16
6825.2.ox $$\chi_{6825}(67, \cdot)$$ n/a 8960 16
6825.2.oz $$\chi_{6825}(358, \cdot)$$ n/a 6720 16
6825.2.pa $$\chi_{6825}(167, \cdot)$$ n/a 17792 16
6825.2.pc $$\chi_{6825}(353, \cdot)$$ n/a 17792 16
6825.2.pe $$\chi_{6825}(772, \cdot)$$ n/a 8960 16
6825.2.ph $$\chi_{6825}(37, \cdot)$$ n/a 8960 16
6825.2.pi $$\chi_{6825}(227, \cdot)$$ n/a 17792 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6825))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6825)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(455))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(975))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1365))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2275))$$$$^{\oplus 2}$$