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Properties

Label 9282.2
Level 9282
Weight 2
Dimension 545983
Nonzero newspaces 180
Sturm bound 9289728

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Defining parameters

Level: \( N \) = \( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 180 \)
Sturm bound: \(9289728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9282))\).

Total New Old
Modular forms 2340864 545983 1794881
Cusp forms 2304001 545983 1758018
Eisenstein series 36863 0 36863

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9282))\)

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
9282.2.a \(\chi_{9282}(1, \cdot)\) 9282.2.a.a 1 1
9282.2.a.b 1
9282.2.a.c 1
9282.2.a.d 1
9282.2.a.e 1
9282.2.a.f 1
9282.2.a.g 1
9282.2.a.h 1
9282.2.a.i 1
9282.2.a.j 1
9282.2.a.k 1
9282.2.a.l 1
9282.2.a.m 1
9282.2.a.n 1
9282.2.a.o 1
9282.2.a.p 1
9282.2.a.q 1
9282.2.a.r 1
9282.2.a.s 1
9282.2.a.t 1
9282.2.a.u 1
9282.2.a.v 1
9282.2.a.w 1
9282.2.a.x 1
9282.2.a.y 2
9282.2.a.z 2
9282.2.a.ba 3
9282.2.a.bb 3
9282.2.a.bc 3
9282.2.a.bd 3
9282.2.a.be 3
9282.2.a.bf 3
9282.2.a.bg 3
9282.2.a.bh 3
9282.2.a.bi 4
9282.2.a.bj 4
9282.2.a.bk 4
9282.2.a.bl 4
9282.2.a.bm 4
9282.2.a.bn 4
9282.2.a.bo 4
9282.2.a.bp 4
9282.2.a.bq 5
9282.2.a.br 5
9282.2.a.bs 5
9282.2.a.bt 5
9282.2.a.bu 5
9282.2.a.bv 6
9282.2.a.bw 6
9282.2.a.bx 6
9282.2.a.by 6
9282.2.a.bz 7
9282.2.a.ca 7
9282.2.a.cb 7
9282.2.a.cc 7
9282.2.a.cd 7
9282.2.a.ce 7
9282.2.a.cf 8
9282.2.a.cg 8
9282.2.b \(\chi_{9282}(1429, \cdot)\) n/a 224 1
9282.2.d \(\chi_{9282}(8737, \cdot)\) n/a 216 1
9282.2.g \(\chi_{9282}(7853, \cdot)\) n/a 576 1
9282.2.i \(\chi_{9282}(545, \cdot)\) n/a 592 1
9282.2.j \(\chi_{9282}(8399, \cdot)\) n/a 512 1
9282.2.l \(\chi_{9282}(9281, \cdot)\) n/a 672 1
9282.2.o \(\chi_{9282}(883, \cdot)\) n/a 248 1
9282.2.q \(\chi_{9282}(1327, \cdot)\) n/a 512 2
9282.2.r \(\chi_{9282}(4897, \cdot)\) n/a 600 2
9282.2.s \(\chi_{9282}(919, \cdot)\) n/a 600 2
9282.2.t \(\chi_{9282}(3571, \cdot)\) n/a 448 2
9282.2.v \(\chi_{9282}(3515, \cdot)\) n/a 1008 2
9282.2.w \(\chi_{9282}(5725, \cdot)\) n/a 672 2
9282.2.y \(\chi_{9282}(3821, \cdot)\) n/a 1344 2
9282.2.bb \(\chi_{9282}(3277, \cdot)\) n/a 432 2
9282.2.bd \(\chi_{9282}(6833, \cdot)\) n/a 1008 2
9282.2.be \(\chi_{9282}(307, \cdot)\) n/a 608 2
9282.2.bh \(\chi_{9282}(239, \cdot)\) n/a 896 2
9282.2.bi \(\chi_{9282}(1903, \cdot)\) n/a 672 2
9282.2.bl \(\chi_{9282}(4705, \cdot)\) n/a 496 2
9282.2.bm \(\chi_{9282}(2393, \cdot)\) n/a 1152 2
9282.2.bp \(\chi_{9282}(3583, \cdot)\) n/a 672 2
9282.2.bq \(\chi_{9282}(1373, \cdot)\) n/a 1008 2
9282.2.bt \(\chi_{9282}(1973, \cdot)\) n/a 1200 2
9282.2.bv \(\chi_{9282}(2141, \cdot)\) n/a 1344 2
9282.2.bw \(\chi_{9282}(3025, \cdot)\) n/a 512 2
9282.2.by \(\chi_{9282}(2857, \cdot)\) n/a 448 2
9282.2.cb \(\chi_{9282}(5339, \cdot)\) n/a 1192 2
9282.2.cd \(\chi_{9282}(101, \cdot)\) n/a 1344 2
9282.2.cg \(\chi_{9282}(7921, \cdot)\) n/a 672 2
9282.2.ci \(\chi_{9282}(2209, \cdot)\) n/a 672 2
9282.2.cl \(\chi_{9282}(2651, \cdot)\) n/a 1344 2
9282.2.cn \(\chi_{9282}(4079, \cdot)\) n/a 1344 2
9282.2.cp \(\chi_{9282}(341, \cdot)\) n/a 1192 2
9282.2.cr \(\chi_{9282}(1769, \cdot)\) n/a 1024 2
9282.2.cs \(\chi_{9282}(3637, \cdot)\) n/a 672 2
9282.2.cw \(\chi_{9282}(4183, \cdot)\) n/a 600 2
9282.2.cy \(\chi_{9282}(373, \cdot)\) n/a 672 2
9282.2.cz \(\chi_{9282}(4625, \cdot)\) n/a 1192 2
9282.2.db \(\chi_{9282}(3197, \cdot)\) n/a 1200 2
9282.2.dd \(\chi_{9282}(1223, \cdot)\) n/a 1152 2
9282.2.df \(\chi_{9282}(815, \cdot)\) n/a 1344 2
9282.2.di \(\chi_{9282}(4351, \cdot)\) n/a 672 2
9282.2.dk \(\chi_{9282}(781, \cdot)\) n/a 576 2
9282.2.dm \(\chi_{9282}(2755, \cdot)\) n/a 592 2
9282.2.do \(\chi_{9282}(205, \cdot)\) n/a 600 2
9282.2.dp \(\chi_{9282}(4793, \cdot)\) n/a 1344 2
9282.2.dr \(\chi_{9282}(647, \cdot)\) n/a 1192 2
9282.2.dv \(\chi_{9282}(2311, \cdot)\) n/a 496 2
9282.2.dw \(\chi_{9282}(1427, \cdot)\) n/a 1344 2
9282.2.dy \(\chi_{9282}(2687, \cdot)\) n/a 1200 2
9282.2.eb \(\chi_{9282}(1919, \cdot)\) n/a 2016 4
9282.2.ec \(\chi_{9282}(2491, \cdot)\) n/a 1344 4
9282.2.ef \(\chi_{9282}(2185, \cdot)\) n/a 864 4
9282.2.eh \(\chi_{9282}(1301, \cdot)\) n/a 2304 4
9282.2.ei \(\chi_{9282}(3613, \cdot)\) n/a 1024 4
9282.2.ek \(\chi_{9282}(2729, \cdot)\) n/a 2688 4
9282.2.em \(\chi_{9282}(281, \cdot)\) n/a 2016 4
9282.2.ep \(\chi_{9282}(4129, \cdot)\) n/a 1344 4
9282.2.eq \(\chi_{9282}(3625, \cdot)\) n/a 1344 4
9282.2.et \(\chi_{9282}(1415, \cdot)\) n/a 2016 4
9282.2.eu \(\chi_{9282}(115, \cdot)\) n/a 1344 4
9282.2.ey \(\chi_{9282}(2699, \cdot)\) n/a 2688 4
9282.2.ez \(\chi_{9282}(3413, \cdot)\) n/a 2688 4
9282.2.fa \(\chi_{9282}(1279, \cdot)\) n/a 1344 4
9282.2.fb \(\chi_{9282}(2971, \cdot)\) n/a 1344 4
9282.2.ff \(\chi_{9282}(557, \cdot)\) n/a 2688 4
9282.2.fg \(\chi_{9282}(3175, \cdot)\) n/a 1344 4
9282.2.fj \(\chi_{9282}(2903, \cdot)\) n/a 2688 4
9282.2.fk \(\chi_{9282}(1135, \cdot)\) n/a 992 4
9282.2.fn \(\chi_{9282}(965, \cdot)\) n/a 2688 4
9282.2.fo \(\chi_{9282}(1067, \cdot)\) n/a 2304 4
9282.2.fr \(\chi_{9282}(2053, \cdot)\) n/a 1344 4
9282.2.ft \(\chi_{9282}(3617, \cdot)\) n/a 2688 4
9282.2.fu \(\chi_{9282}(2461, \cdot)\) n/a 1344 4
9282.2.fx \(\chi_{9282}(409, \cdot)\) n/a 1200 4
9282.2.fy \(\chi_{9282}(305, \cdot)\) n/a 2688 4
9282.2.ga \(\chi_{9282}(2381, \cdot)\) n/a 1792 4
9282.2.gd \(\chi_{9282}(475, \cdot)\) n/a 1344 4
9282.2.ge \(\chi_{9282}(577, \cdot)\) n/a 1344 4
9282.2.gh \(\chi_{9282}(1565, \cdot)\) n/a 2400 4
9282.2.gj \(\chi_{9282}(2719, \cdot)\) n/a 1344 4
9282.2.gk \(\chi_{9282}(3707, \cdot)\) n/a 2384 4
9282.2.gm \(\chi_{9282}(1835, \cdot)\) n/a 2016 4
9282.2.gp \(\chi_{9282}(1021, \cdot)\) n/a 1184 4
9282.2.gr \(\chi_{9282}(3265, \cdot)\) n/a 1200 4
9282.2.gs \(\chi_{9282}(3161, \cdot)\) n/a 2688 4
9282.2.gu \(\chi_{9282}(1123, \cdot)\) n/a 1184 4
9282.2.gx \(\chi_{9282}(1019, \cdot)\) n/a 2688 4
9282.2.gz \(\chi_{9282}(271, \cdot)\) n/a 1344 4
9282.2.ha \(\chi_{9282}(137, \cdot)\) n/a 2384 4
9282.2.hd \(\chi_{9282}(251, \cdot)\) n/a 2688 4
9282.2.he \(\chi_{9282}(1849, \cdot)\) n/a 1024 4
9282.2.hh \(\chi_{9282}(625, \cdot)\) n/a 1152 4
9282.2.hi \(\chi_{9282}(2495, \cdot)\) n/a 2688 4
9282.2.hk \(\chi_{9282}(1075, \cdot)\) n/a 1344 4
9282.2.hn \(\chi_{9282}(803, \cdot)\) n/a 2688 4
9282.2.hp \(\chi_{9282}(1517, \cdot)\) n/a 2688 4
9282.2.hq \(\chi_{9282}(361, \cdot)\) n/a 1344 4
9282.2.hs \(\chi_{9282}(149, \cdot)\) n/a 2688 4
9282.2.hw \(\chi_{9282}(1237, \cdot)\) n/a 1344 4
9282.2.hx \(\chi_{9282}(4399, \cdot)\) n/a 1344 4
9282.2.hy \(\chi_{9282}(3005, \cdot)\) n/a 2688 4
9282.2.hz \(\chi_{9282}(863, \cdot)\) n/a 2688 4
9282.2.id \(\chi_{9282}(2299, \cdot)\) n/a 1344 4
9282.2.ie \(\chi_{9282}(2087, \cdot)\) n/a 2016 4
9282.2.ih \(\chi_{9282}(769, \cdot)\) n/a 1344 4
9282.2.ik \(\chi_{9282}(1009, \cdot)\) n/a 2016 8
9282.2.il \(\chi_{9282}(125, \cdot)\) n/a 5376 8
9282.2.io \(\chi_{9282}(2029, \cdot)\) n/a 2304 8
9282.2.ip \(\chi_{9282}(911, \cdot)\) n/a 3456 8
9282.2.is \(\chi_{9282}(181, \cdot)\) n/a 2688 8
9282.2.it \(\chi_{9282}(1247, \cdot)\) n/a 4032 8
9282.2.iw \(\chi_{9282}(2647, \cdot)\) n/a 2016 8
9282.2.ix \(\chi_{9282}(1763, \cdot)\) n/a 5376 8
9282.2.iz \(\chi_{9282}(19, \cdot)\) n/a 2688 8
9282.2.ja \(\chi_{9282}(977, \cdot)\) n/a 5376 8
9282.2.jd \(\chi_{9282}(1409, \cdot)\) n/a 5376 8
9282.2.jf \(\chi_{9282}(1861, \cdot)\) n/a 2688 8
9282.2.jh \(\chi_{9282}(145, \cdot)\) n/a 2688 8
9282.2.ji \(\chi_{9282}(2321, \cdot)\) n/a 5376 8
9282.2.jk \(\chi_{9282}(995, \cdot)\) n/a 4032 8
9282.2.jm \(\chi_{9282}(2371, \cdot)\) n/a 2688 8
9282.2.jo \(\chi_{9282}(1511, \cdot)\) n/a 5376 8
9282.2.jq \(\chi_{9282}(757, \cdot)\) n/a 1984 8
9282.2.jt \(\chi_{9282}(25, \cdot)\) n/a 2688 8
9282.2.ju \(\chi_{9282}(1811, \cdot)\) n/a 5376 8
9282.2.jw \(\chi_{9282}(257, \cdot)\) n/a 5376 8
9282.2.jy \(\chi_{9282}(121, \cdot)\) n/a 2688 8
9282.2.ka \(\chi_{9282}(1369, \cdot)\) n/a 2688 8
9282.2.kd \(\chi_{9282}(467, \cdot)\) n/a 5376 8
9282.2.ke \(\chi_{9282}(1171, \cdot)\) n/a 2304 8
9282.2.kh \(\chi_{9282}(2525, \cdot)\) n/a 5376 8
9282.2.kj \(\chi_{9282}(185, \cdot)\) n/a 5376 8
9282.2.kl \(\chi_{9282}(529, \cdot)\) n/a 2688 8
9282.2.kn \(\chi_{9282}(2083, \cdot)\) n/a 2688 8
9282.2.ko \(\chi_{9282}(1613, \cdot)\) n/a 4608 8
9282.2.kr \(\chi_{9282}(797, \cdot)\) n/a 5376 8
9282.2.kt \(\chi_{9282}(43, \cdot)\) n/a 2048 8
9282.2.ku \(\chi_{9282}(359, \cdot)\) n/a 5376 8
9282.2.kw \(\chi_{9282}(1783, \cdot)\) n/a 2688 8
9282.2.ky \(\chi_{9282}(223, \cdot)\) n/a 2688 8
9282.2.lb \(\chi_{9282}(869, \cdot)\) n/a 4032 8
9282.2.ld \(\chi_{9282}(1913, \cdot)\) n/a 5376 8
9282.2.lf \(\chi_{9282}(229, \cdot)\) n/a 2688 8
9282.2.lg \(\chi_{9282}(535, \cdot)\) n/a 2688 8
9282.2.lj \(\chi_{9282}(695, \cdot)\) n/a 5376 8
9282.2.lk \(\chi_{9282}(379, \cdot)\) n/a 4032 16
9282.2.ll \(\chi_{9282}(839, \cdot)\) n/a 10752 16
9282.2.lo \(\chi_{9282}(227, \cdot)\) n/a 10752 16
9282.2.lp \(\chi_{9282}(37, \cdot)\) n/a 5376 16
9282.2.lu \(\chi_{9282}(437, \cdot)\) n/a 10752 16
9282.2.lv \(\chi_{9282}(109, \cdot)\) n/a 5376 16
9282.2.ly \(\chi_{9282}(479, \cdot)\) n/a 10752 16
9282.2.lz \(\chi_{9282}(709, \cdot)\) n/a 5376 16
9282.2.mc \(\chi_{9282}(737, \cdot)\) n/a 10752 16
9282.2.md \(\chi_{9282}(61, \cdot)\) n/a 5376 16
9282.2.me \(\chi_{9282}(517, \cdot)\) n/a 5376 16
9282.2.mf \(\chi_{9282}(233, \cdot)\) n/a 10752 16
9282.2.mg \(\chi_{9282}(23, \cdot)\) n/a 10752 16
9282.2.mh \(\chi_{9282}(199, \cdot)\) n/a 5376 16
9282.2.mi \(\chi_{9282}(649, \cdot)\) n/a 5376 16
9282.2.mj \(\chi_{9282}(1499, \cdot)\) n/a 8064 16
9282.2.mq \(\chi_{9282}(139, \cdot)\) n/a 5376 16
9282.2.mr \(\chi_{9282}(107, \cdot)\) n/a 10752 16
9282.2.ms \(\chi_{9282}(989, \cdot)\) n/a 9216 16
9282.2.mt \(\chi_{9282}(313, \cdot)\) n/a 4608 16
9282.2.mu \(\chi_{9282}(997, \cdot)\) n/a 5376 16
9282.2.mv \(\chi_{9282}(29, \cdot)\) n/a 8064 16
9282.2.ne \(\chi_{9282}(725, \cdot)\) n/a 10752 16
9282.2.nf \(\chi_{9282}(283, \cdot)\) n/a 5376 16
9282.2.ni \(\chi_{9282}(5, \cdot)\) n/a 10752 16
9282.2.nj \(\chi_{9282}(2137, \cdot)\) n/a 5376 16
9282.2.nm \(\chi_{9282}(215, \cdot)\) n/a 10752 16
9282.2.nn \(\chi_{9282}(163, \cdot)\) n/a 5376 16
9282.2.no \(\chi_{9282}(605, \cdot)\) n/a 10752 16
9282.2.np \(\chi_{9282}(1129, \cdot)\) n/a 5376 16
9282.2.ns \(\chi_{9282}(505, \cdot)\) n/a 4032 16
9282.2.nt \(\chi_{9282}(41, \cdot)\) n/a 10752 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9282))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9282)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(442))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(663))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1326))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1547))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3094))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4641))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9282))\)\(^{\oplus 1}\)