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Properties

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

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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 available 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

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