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Properties

Label 9225.2
Level 9225
Weight 2
Dimension 2196648
Nonzero newspaces 196
Sturm bound 12096000

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Defining parameters

Level: \( N \) = \( 9225 = 3^{2} \cdot 5^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 196 \)
Sturm bound: \(12096000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9225))\).

Total New Old
Modular forms 3041920 2211038 830882
Cusp forms 3006081 2196648 809433
Eisenstein series 35839 14390 21449

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9225))\)

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
9225.2.a \(\chi_{9225}(1, \cdot)\) 9225.2.a.a 1 1
9225.2.a.b 1
9225.2.a.c 1
9225.2.a.d 1
9225.2.a.e 1
9225.2.a.f 1
9225.2.a.g 1
9225.2.a.h 1
9225.2.a.i 1
9225.2.a.j 1
9225.2.a.k 1
9225.2.a.l 1
9225.2.a.m 1
9225.2.a.n 1
9225.2.a.o 1
9225.2.a.p 1
9225.2.a.q 1
9225.2.a.r 1
9225.2.a.s 1
9225.2.a.t 1
9225.2.a.u 1
9225.2.a.v 1
9225.2.a.w 1
9225.2.a.x 1
9225.2.a.y 1
9225.2.a.z 1
9225.2.a.ba 1
9225.2.a.bb 1
9225.2.a.bc 1
9225.2.a.bd 1
9225.2.a.be 1
9225.2.a.bf 2
9225.2.a.bg 2
9225.2.a.bh 2
9225.2.a.bi 2
9225.2.a.bj 2
9225.2.a.bk 2
9225.2.a.bl 2
9225.2.a.bm 2
9225.2.a.bn 2
9225.2.a.bo 2
9225.2.a.bp 2
9225.2.a.bq 2
9225.2.a.br 3
9225.2.a.bs 3
9225.2.a.bt 3
9225.2.a.bu 3
9225.2.a.bv 3
9225.2.a.bw 3
9225.2.a.bx 3
9225.2.a.by 3
9225.2.a.bz 3
9225.2.a.ca 3
9225.2.a.cb 3
9225.2.a.cc 3
9225.2.a.cd 4
9225.2.a.ce 4
9225.2.a.cf 4
9225.2.a.cg 5
9225.2.a.ch 5
9225.2.a.ci 5
9225.2.a.cj 6
9225.2.a.ck 6
9225.2.a.cl 7
9225.2.a.cm 7
9225.2.a.cn 7
9225.2.a.co 7
9225.2.a.cp 7
9225.2.a.cq 7
9225.2.a.cr 7
9225.2.a.cs 7
9225.2.a.ct 8
9225.2.a.cu 9
9225.2.a.cv 9
9225.2.a.cw 9
9225.2.a.cx 9
9225.2.a.cy 10
9225.2.a.cz 10
9225.2.a.da 10
9225.2.a.db 10
9225.2.a.dc 14
9225.2.a.dd 16
9225.2.a.de 16
9225.2.b \(\chi_{9225}(6274, \cdot)\) n/a 300 1
9225.2.e \(\chi_{9225}(7174, \cdot)\) n/a 312 1
9225.2.f \(\chi_{9225}(901, \cdot)\) n/a 330 1
9225.2.i \(\chi_{9225}(3076, \cdot)\) n/a 1520 2
9225.2.k \(\chi_{9225}(4501, \cdot)\) n/a 658 2
9225.2.l \(\chi_{9225}(3968, \cdot)\) n/a 504 2
9225.2.n \(\chi_{9225}(1682, \cdot)\) n/a 480 2
9225.2.q \(\chi_{9225}(368, \cdot)\) n/a 504 2
9225.2.s \(\chi_{9225}(5093, \cdot)\) n/a 504 2
9225.2.t \(\chi_{9225}(1549, \cdot)\) n/a 628 2
9225.2.v \(\chi_{9225}(406, \cdot)\) n/a 2088 4
9225.2.w \(\chi_{9225}(1576, \cdot)\) n/a 1320 4
9225.2.x \(\chi_{9225}(4321, \cdot)\) n/a 2088 4
9225.2.y \(\chi_{9225}(3331, \cdot)\) n/a 2088 4
9225.2.z \(\chi_{9225}(1846, \cdot)\) n/a 2000 4
9225.2.ba \(\chi_{9225}(631, \cdot)\) n/a 2088 4
9225.2.bc \(\chi_{9225}(3976, \cdot)\) n/a 1584 2
9225.2.bf \(\chi_{9225}(1024, \cdot)\) n/a 1504 2
9225.2.bg \(\chi_{9225}(124, \cdot)\) n/a 1440 2
9225.2.bj \(\chi_{9225}(3007, \cdot)\) n/a 1252 4
9225.2.bk \(\chi_{9225}(899, \cdot)\) n/a 1008 4
9225.2.bn \(\chi_{9225}(1151, \cdot)\) n/a 1064 4
9225.2.bo \(\chi_{9225}(793, \cdot)\) n/a 1252 4
9225.2.br \(\chi_{9225}(1234, \cdot)\) n/a 2096 4
9225.2.bs \(\chi_{9225}(1369, \cdot)\) n/a 2096 4
9225.2.bv \(\chi_{9225}(2746, \cdot)\) n/a 2088 4
9225.2.cb \(\chi_{9225}(496, \cdot)\) n/a 2088 4
9225.2.cd \(\chi_{9225}(271, \cdot)\) n/a 2088 4
9225.2.cf \(\chi_{9225}(4951, \cdot)\) n/a 1320 4
9225.2.ch \(\chi_{9225}(3016, \cdot)\) n/a 2088 4
9225.2.ck \(\chi_{9225}(739, \cdot)\) n/a 2000 4
9225.2.cl \(\chi_{9225}(64, \cdot)\) n/a 2096 4
9225.2.cn \(\chi_{9225}(1999, \cdot)\) n/a 1248 4
9225.2.cp \(\chi_{9225}(154, \cdot)\) n/a 2096 4
9225.2.cr \(\chi_{9225}(2854, \cdot)\) n/a 2096 4
9225.2.cu \(\chi_{9225}(469, \cdot)\) n/a 2096 4
9225.2.cw \(\chi_{9225}(379, \cdot)\) n/a 2096 4
9225.2.cy \(\chi_{9225}(2224, \cdot)\) n/a 1248 4
9225.2.da \(\chi_{9225}(2314, \cdot)\) n/a 2096 4
9225.2.db \(\chi_{9225}(1639, \cdot)\) n/a 2096 4
9225.2.de \(\chi_{9225}(1171, \cdot)\) n/a 2088 4
9225.2.dg \(\chi_{9225}(4624, \cdot)\) n/a 3008 4
9225.2.dj \(\chi_{9225}(32, \cdot)\) n/a 3008 4
9225.2.dl \(\chi_{9225}(3443, \cdot)\) n/a 3008 4
9225.2.dm \(\chi_{9225}(2543, \cdot)\) n/a 2880 4
9225.2.do \(\chi_{9225}(893, \cdot)\) n/a 3008 4
9225.2.dr \(\chi_{9225}(1426, \cdot)\) n/a 3168 4
9225.2.ds \(\chi_{9225}(346, \cdot)\) n/a 10048 8
9225.2.dt \(\chi_{9225}(616, \cdot)\) n/a 9600 8
9225.2.du \(\chi_{9225}(16, \cdot)\) n/a 10048 8
9225.2.dv \(\chi_{9225}(1246, \cdot)\) n/a 10048 8
9225.2.dw \(\chi_{9225}(2101, \cdot)\) n/a 6336 8
9225.2.dx \(\chi_{9225}(871, \cdot)\) n/a 10048 8
9225.2.dy \(\chi_{9225}(361, \cdot)\) n/a 4192 8
9225.2.ea \(\chi_{9225}(289, \cdot)\) n/a 4176 8
9225.2.ef \(\chi_{9225}(964, \cdot)\) n/a 4176 8
9225.2.eg \(\chi_{9225}(1099, \cdot)\) n/a 2512 8
9225.2.eh \(\chi_{9225}(244, \cdot)\) n/a 4176 8
9225.2.ei \(\chi_{9225}(829, \cdot)\) n/a 4176 8
9225.2.el \(\chi_{9225}(2537, \cdot)\) n/a 3360 8
9225.2.em \(\chi_{9225}(1583, \cdot)\) n/a 3360 8
9225.2.ep \(\chi_{9225}(467, \cdot)\) n/a 3360 8
9225.2.eq \(\chi_{9225}(377, \cdot)\) n/a 3360 8
9225.2.et \(\chi_{9225}(278, \cdot)\) n/a 3360 8
9225.2.eu \(\chi_{9225}(3887, \cdot)\) n/a 3360 8
9225.2.ew \(\chi_{9225}(197, \cdot)\) n/a 3360 8
9225.2.ex \(\chi_{9225}(8, \cdot)\) n/a 3360 8
9225.2.ey \(\chi_{9225}(818, \cdot)\) n/a 2016 8
9225.2.fc \(\chi_{9225}(2312, \cdot)\) n/a 3360 8
9225.2.fe \(\chi_{9225}(107, \cdot)\) n/a 2016 8
9225.2.fg \(\chi_{9225}(638, \cdot)\) n/a 3360 8
9225.2.fh \(\chi_{9225}(2177, \cdot)\) n/a 3360 8
9225.2.fi \(\chi_{9225}(737, \cdot)\) n/a 3360 8
9225.2.fp \(\chi_{9225}(1313, \cdot)\) n/a 3200 8
9225.2.fq \(\chi_{9225}(4733, \cdot)\) n/a 3360 8
9225.2.fr \(\chi_{9225}(98, \cdot)\) n/a 3360 8
9225.2.ft \(\chi_{9225}(1043, \cdot)\) n/a 2016 8
9225.2.fv \(\chi_{9225}(2852, \cdot)\) n/a 3360 8
9225.2.fz \(\chi_{9225}(143, \cdot)\) n/a 2016 8
9225.2.ga \(\chi_{9225}(62, \cdot)\) n/a 3360 8
9225.2.gb \(\chi_{9225}(863, \cdot)\) n/a 3360 8
9225.2.gd \(\chi_{9225}(323, \cdot)\) n/a 3360 8
9225.2.ge \(\chi_{9225}(647, \cdot)\) n/a 3360 8
9225.2.gh \(\chi_{9225}(91, \cdot)\) n/a 4192 8
9225.2.gi \(\chi_{9225}(226, \cdot)\) n/a 2632 8
9225.2.gj \(\chi_{9225}(856, \cdot)\) n/a 4192 8
9225.2.gk \(\chi_{9225}(541, \cdot)\) n/a 4192 8
9225.2.gp \(\chi_{9225}(46, \cdot)\) n/a 4192 8
9225.2.gr \(\chi_{9225}(784, \cdot)\) n/a 4176 8
9225.2.gt \(\chi_{9225}(1093, \cdot)\) n/a 6016 8
9225.2.gv \(\chi_{9225}(776, \cdot)\) n/a 6336 8
9225.2.gw \(\chi_{9225}(1274, \cdot)\) n/a 6016 8
9225.2.gy \(\chi_{9225}(232, \cdot)\) n/a 6016 8
9225.2.ha \(\chi_{9225}(2731, \cdot)\) n/a 10048 8
9225.2.hd \(\chi_{9225}(409, \cdot)\) n/a 10048 8
9225.2.hg \(\chi_{9225}(529, \cdot)\) n/a 10048 8
9225.2.hi \(\chi_{9225}(1699, \cdot)\) n/a 6016 8
9225.2.hk \(\chi_{9225}(139, \cdot)\) n/a 10048 8
9225.2.hm \(\chi_{9225}(754, \cdot)\) n/a 10048 8
9225.2.hn \(\chi_{9225}(1294, \cdot)\) n/a 10048 8
9225.2.hp \(\chi_{9225}(619, \cdot)\) n/a 10048 8
9225.2.hr \(\chi_{9225}(1624, \cdot)\) n/a 6016 8
9225.2.ht \(\chi_{9225}(4, \cdot)\) n/a 10048 8
9225.2.hw \(\chi_{9225}(1354, \cdot)\) n/a 9600 8
9225.2.hz \(\chi_{9225}(646, \cdot)\) n/a 10048 8
9225.2.ib \(\chi_{9225}(1501, \cdot)\) n/a 6336 8
9225.2.id \(\chi_{9225}(556, \cdot)\) n/a 10048 8
9225.2.if \(\chi_{9225}(31, \cdot)\) n/a 10048 8
9225.2.il \(\chi_{9225}(286, \cdot)\) n/a 10048 8
9225.2.im \(\chi_{9225}(1759, \cdot)\) n/a 10048 8
9225.2.ip \(\chi_{9225}(394, \cdot)\) n/a 10048 8
9225.2.iq \(\chi_{9225}(28, \cdot)\) n/a 8368 16
9225.2.is \(\chi_{9225}(478, \cdot)\) n/a 8368 16
9225.2.ix \(\chi_{9225}(622, \cdot)\) n/a 8368 16
9225.2.iy \(\chi_{9225}(343, \cdot)\) n/a 5008 16
9225.2.iz \(\chi_{9225}(388, \cdot)\) n/a 8368 16
9225.2.ja \(\chi_{9225}(217, \cdot)\) n/a 8368 16
9225.2.jd \(\chi_{9225}(404, \cdot)\) n/a 6720 16
9225.2.je \(\chi_{9225}(386, \cdot)\) n/a 6720 16
9225.2.jh \(\chi_{9225}(1196, \cdot)\) n/a 6720 16
9225.2.ji \(\chi_{9225}(26, \cdot)\) n/a 4256 16
9225.2.jj \(\chi_{9225}(161, \cdot)\) n/a 6720 16
9225.2.jk \(\chi_{9225}(71, \cdot)\) n/a 6720 16
9225.2.jp \(\chi_{9225}(116, \cdot)\) n/a 6720 16
9225.2.jq \(\chi_{9225}(179, \cdot)\) n/a 6720 16
9225.2.jv \(\chi_{9225}(134, \cdot)\) n/a 6720 16
9225.2.jw \(\chi_{9225}(44, \cdot)\) n/a 6720 16
9225.2.jx \(\chi_{9225}(89, \cdot)\) n/a 6720 16
9225.2.jy \(\chi_{9225}(224, \cdot)\) n/a 4032 16
9225.2.kb \(\chi_{9225}(253, \cdot)\) n/a 8368 16
9225.2.kc \(\chi_{9225}(937, \cdot)\) n/a 8368 16
9225.2.kd \(\chi_{9225}(1297, \cdot)\) n/a 8368 16
9225.2.ke \(\chi_{9225}(757, \cdot)\) n/a 5008 16
9225.2.kj \(\chi_{9225}(208, \cdot)\) n/a 8368 16
9225.2.kl \(\chi_{9225}(397, \cdot)\) n/a 8368 16
9225.2.kn \(\chi_{9225}(664, \cdot)\) n/a 20096 16
9225.2.kp \(\chi_{9225}(661, \cdot)\) n/a 20096 16
9225.2.kq \(\chi_{9225}(976, \cdot)\) n/a 12672 16
9225.2.kr \(\chi_{9225}(61, \cdot)\) n/a 20096 16
9225.2.ks \(\chi_{9225}(196, \cdot)\) n/a 20096 16
9225.2.kx \(\chi_{9225}(736, \cdot)\) n/a 20096 16
9225.2.ky \(\chi_{9225}(173, \cdot)\) n/a 20096 16
9225.2.lb \(\chi_{9225}(2288, \cdot)\) n/a 20096 16
9225.2.lf \(\chi_{9225}(677, \cdot)\) n/a 20096 16
9225.2.lg \(\chi_{9225}(443, \cdot)\) n/a 12032 16
9225.2.lh \(\chi_{9225}(248, \cdot)\) n/a 20096 16
9225.2.lj \(\chi_{9225}(23, \cdot)\) n/a 20096 16
9225.2.ll \(\chi_{9225}(182, \cdot)\) n/a 12032 16
9225.2.lp \(\chi_{9225}(83, \cdot)\) n/a 19200 16
9225.2.lq \(\chi_{9225}(2333, \cdot)\) n/a 20096 16
9225.2.lr \(\chi_{9225}(338, \cdot)\) n/a 20096 16
9225.2.ls \(\chi_{9225}(113, \cdot)\) n/a 20096 16
9225.2.lt \(\chi_{9225}(2198, \cdot)\) n/a 20096 16
9225.2.lu \(\chi_{9225}(122, \cdot)\) n/a 20096 16
9225.2.ly \(\chi_{9225}(482, \cdot)\) n/a 12032 16
9225.2.ma \(\chi_{9225}(92, \cdot)\) n/a 20096 16
9225.2.mc \(\chi_{9225}(2, \cdot)\) n/a 20096 16
9225.2.md \(\chi_{9225}(743, \cdot)\) n/a 12032 16
9225.2.me \(\chi_{9225}(923, \cdot)\) n/a 20096 16
9225.2.mi \(\chi_{9225}(77, \cdot)\) n/a 20096 16
9225.2.ml \(\chi_{9225}(542, \cdot)\) n/a 20096 16
9225.2.mm \(\chi_{9225}(572, \cdot)\) n/a 20096 16
9225.2.mp \(\chi_{9225}(428, \cdot)\) n/a 20096 16
9225.2.mq \(\chi_{9225}(1253, \cdot)\) n/a 20096 16
9225.2.mt \(\chi_{9225}(203, \cdot)\) n/a 20096 16
9225.2.mu \(\chi_{9225}(184, \cdot)\) n/a 20096 16
9225.2.mz \(\chi_{9225}(214, \cdot)\) n/a 20096 16
9225.2.na \(\chi_{9225}(364, \cdot)\) n/a 20096 16
9225.2.nb \(\chi_{9225}(169, \cdot)\) n/a 20096 16
9225.2.nc \(\chi_{9225}(49, \cdot)\) n/a 12032 16
9225.2.ne \(\chi_{9225}(121, \cdot)\) n/a 20096 16
9225.2.ng \(\chi_{9225}(52, \cdot)\) n/a 40192 32
9225.2.ni \(\chi_{9225}(448, \cdot)\) n/a 40192 32
9225.2.nn \(\chi_{9225}(97, \cdot)\) n/a 40192 32
9225.2.no \(\chi_{9225}(13, \cdot)\) n/a 40192 32
9225.2.np \(\chi_{9225}(193, \cdot)\) n/a 24064 32
9225.2.nq \(\chi_{9225}(22, \cdot)\) n/a 40192 32
9225.2.ns \(\chi_{9225}(29, \cdot)\) n/a 40192 32
9225.2.nx \(\chi_{9225}(149, \cdot)\) n/a 24064 32
9225.2.ny \(\chi_{9225}(239, \cdot)\) n/a 40192 32
9225.2.nz \(\chi_{9225}(14, \cdot)\) n/a 40192 32
9225.2.oa \(\chi_{9225}(104, \cdot)\) n/a 40192 32
9225.2.od \(\chi_{9225}(56, \cdot)\) n/a 40192 32
9225.2.oe \(\chi_{9225}(191, \cdot)\) n/a 40192 32
9225.2.of \(\chi_{9225}(101, \cdot)\) n/a 25344 32
9225.2.og \(\chi_{9225}(281, \cdot)\) n/a 40192 32
9225.2.ol \(\chi_{9225}(671, \cdot)\) n/a 40192 32
9225.2.om \(\chi_{9225}(11, \cdot)\) n/a 40192 32
9225.2.op \(\chi_{9225}(479, \cdot)\) n/a 40192 32
9225.2.or \(\chi_{9225}(7, \cdot)\) n/a 24064 32
9225.2.os \(\chi_{9225}(88, \cdot)\) n/a 40192 32
9225.2.ot \(\chi_{9225}(58, \cdot)\) n/a 40192 32
9225.2.ou \(\chi_{9225}(112, \cdot)\) n/a 40192 32
9225.2.oz \(\chi_{9225}(178, \cdot)\) n/a 40192 32
9225.2.pb \(\chi_{9225}(142, \cdot)\) n/a 40192 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(369))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(615))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1025))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1845))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3075))\)\(^{\oplus 2}\)