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Properties

Label 8800.2
Level 8800
Weight 2
Dimension 1170882
Nonzero newspaces 140
Sturm bound 9216000

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Defining parameters

Level: \( N \) = \( 8800 = 2^{5} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 140 \)
Sturm bound: \(9216000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8800))\).

Total New Old
Modular forms 2321920 1178262 1143658
Cusp forms 2286081 1170882 1115199
Eisenstein series 35839 7380 28459

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8800))\)

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
8800.2.a \(\chi_{8800}(1, \cdot)\) 8800.2.a.a 1 1
8800.2.a.b 1
8800.2.a.c 1
8800.2.a.d 1
8800.2.a.e 1
8800.2.a.f 1
8800.2.a.g 1
8800.2.a.h 1
8800.2.a.i 1
8800.2.a.j 1
8800.2.a.k 1
8800.2.a.l 1
8800.2.a.m 1
8800.2.a.n 1
8800.2.a.o 1
8800.2.a.p 1
8800.2.a.q 1
8800.2.a.r 1
8800.2.a.s 1
8800.2.a.t 1
8800.2.a.u 1
8800.2.a.v 1
8800.2.a.w 1
8800.2.a.x 1
8800.2.a.y 1
8800.2.a.z 1
8800.2.a.ba 1
8800.2.a.bb 1
8800.2.a.bc 2
8800.2.a.bd 2
8800.2.a.be 2
8800.2.a.bf 2
8800.2.a.bg 3
8800.2.a.bh 3
8800.2.a.bi 3
8800.2.a.bj 3
8800.2.a.bk 4
8800.2.a.bl 4
8800.2.a.bm 4
8800.2.a.bn 4
8800.2.a.bo 4
8800.2.a.bp 4
8800.2.a.bq 4
8800.2.a.br 4
8800.2.a.bs 5
8800.2.a.bt 5
8800.2.a.bu 5
8800.2.a.bv 5
8800.2.a.bw 5
8800.2.a.bx 5
8800.2.a.by 6
8800.2.a.bz 6
8800.2.a.ca 6
8800.2.a.cb 6
8800.2.a.cc 7
8800.2.a.cd 7
8800.2.a.ce 7
8800.2.a.cf 7
8800.2.a.cg 7
8800.2.a.ch 7
8800.2.a.ci 7
8800.2.a.cj 7
8800.2.b \(\chi_{8800}(8449, \cdot)\) n/a 180 1
8800.2.c \(\chi_{8800}(4399, \cdot)\) n/a 212 1
8800.2.f \(\chi_{8800}(351, \cdot)\) n/a 228 1
8800.2.g \(\chi_{8800}(4401, \cdot)\) n/a 190 1
8800.2.l \(\chi_{8800}(4049, \cdot)\) n/a 180 1
8800.2.m \(\chi_{8800}(8799, \cdot)\) n/a 216 1
8800.2.p \(\chi_{8800}(4751, \cdot)\) n/a 222 1
8800.2.s \(\chi_{8800}(6007, \cdot)\) None 0 2
8800.2.t \(\chi_{8800}(857, \cdot)\) None 0 2
8800.2.v \(\chi_{8800}(2551, \cdot)\) None 0 2
8800.2.w \(\chi_{8800}(2201, \cdot)\) None 0 2
8800.2.z \(\chi_{8800}(5743, \cdot)\) n/a 360 2
8800.2.bb \(\chi_{8800}(593, \cdot)\) n/a 424 2
8800.2.bd \(\chi_{8800}(4993, \cdot)\) n/a 432 2
8800.2.bf \(\chi_{8800}(1343, \cdot)\) n/a 360 2
8800.2.bh \(\chi_{8800}(1849, \cdot)\) None 0 2
8800.2.bi \(\chi_{8800}(2199, \cdot)\) None 0 2
8800.2.bk \(\chi_{8800}(1607, \cdot)\) None 0 2
8800.2.bl \(\chi_{8800}(5257, \cdot)\) None 0 2
8800.2.bo \(\chi_{8800}(2561, \cdot)\) n/a 1440 4
8800.2.bp \(\chi_{8800}(801, \cdot)\) n/a 912 4
8800.2.bq \(\chi_{8800}(641, \cdot)\) n/a 1440 4
8800.2.br \(\chi_{8800}(4481, \cdot)\) n/a 1440 4
8800.2.bs \(\chi_{8800}(1761, \cdot)\) n/a 1200 4
8800.2.bt \(\chi_{8800}(1281, \cdot)\) n/a 1440 4
8800.2.bu \(\chi_{8800}(2443, \cdot)\) n/a 2880 4
8800.2.bx \(\chi_{8800}(3893, \cdot)\) n/a 3440 4
8800.2.by \(\chi_{8800}(1099, \cdot)\) n/a 3440 4
8800.2.ca \(\chi_{8800}(1101, \cdot)\) n/a 3040 4
8800.2.cd \(\chi_{8800}(1451, \cdot)\) n/a 3624 4
8800.2.cf \(\chi_{8800}(749, \cdot)\) n/a 2880 4
8800.2.ch \(\chi_{8800}(1693, \cdot)\) n/a 3440 4
8800.2.ci \(\chi_{8800}(243, \cdot)\) n/a 2880 4
8800.2.ck \(\chi_{8800}(1841, \cdot)\) n/a 1424 4
8800.2.cl \(\chi_{8800}(831, \cdot)\) n/a 1440 4
8800.2.co \(\chi_{8800}(79, \cdot)\) n/a 1424 4
8800.2.cp \(\chi_{8800}(289, \cdot)\) n/a 1440 4
8800.2.cs \(\chi_{8800}(1759, \cdot)\) n/a 1440 4
8800.2.ct \(\chi_{8800}(529, \cdot)\) n/a 1200 4
8800.2.cw \(\chi_{8800}(1711, \cdot)\) n/a 1424 4
8800.2.cx \(\chi_{8800}(431, \cdot)\) n/a 1424 4
8800.2.cy \(\chi_{8800}(271, \cdot)\) n/a 1424 4
8800.2.cz \(\chi_{8800}(2351, \cdot)\) n/a 888 4
8800.2.di \(\chi_{8800}(2929, \cdot)\) n/a 1424 4
8800.2.dj \(\chi_{8800}(799, \cdot)\) n/a 864 4
8800.2.dk \(\chi_{8800}(1119, \cdot)\) n/a 1440 4
8800.2.dl \(\chi_{8800}(479, \cdot)\) n/a 1440 4
8800.2.dm \(\chi_{8800}(1489, \cdot)\) n/a 1424 4
8800.2.dn \(\chi_{8800}(49, \cdot)\) n/a 848 4
8800.2.do \(\chi_{8800}(1169, \cdot)\) n/a 1424 4
8800.2.dp \(\chi_{8800}(959, \cdot)\) n/a 1440 4
8800.2.dy \(\chi_{8800}(1231, \cdot)\) n/a 1424 4
8800.2.ed \(\chi_{8800}(879, \cdot)\) n/a 1424 4
8800.2.ee \(\chi_{8800}(1409, \cdot)\) n/a 1200 4
8800.2.en \(\chi_{8800}(1471, \cdot)\) n/a 1440 4
8800.2.eo \(\chi_{8800}(1681, \cdot)\) n/a 1424 4
8800.2.ep \(\chi_{8800}(401, \cdot)\) n/a 888 4
8800.2.eq \(\chi_{8800}(3281, \cdot)\) n/a 1424 4
8800.2.er \(\chi_{8800}(1151, \cdot)\) n/a 912 4
8800.2.es \(\chi_{8800}(1311, \cdot)\) n/a 1440 4
8800.2.et \(\chi_{8800}(2911, \cdot)\) n/a 1440 4
8800.2.eu \(\chi_{8800}(81, \cdot)\) n/a 1424 4
8800.2.fd \(\chi_{8800}(2209, \cdot)\) n/a 1440 4
8800.2.fe \(\chi_{8800}(3439, \cdot)\) n/a 1424 4
8800.2.ff \(\chi_{8800}(1359, \cdot)\) n/a 1424 4
8800.2.fg \(\chi_{8800}(1999, \cdot)\) n/a 848 4
8800.2.fh \(\chi_{8800}(4129, \cdot)\) n/a 1440 4
8800.2.fi \(\chi_{8800}(449, \cdot)\) n/a 864 4
8800.2.fj \(\chi_{8800}(929, \cdot)\) n/a 1440 4
8800.2.fk \(\chi_{8800}(5359, \cdot)\) n/a 1424 4
8800.2.fn \(\chi_{8800}(881, \cdot)\) n/a 1200 4
8800.2.fo \(\chi_{8800}(2111, \cdot)\) n/a 1440 4
8800.2.fr \(\chi_{8800}(3791, \cdot)\) n/a 1424 4
8800.2.fu \(\chi_{8800}(2559, \cdot)\) n/a 1440 4
8800.2.fv \(\chi_{8800}(1329, \cdot)\) n/a 1424 4
8800.2.fy \(\chi_{8800}(1977, \cdot)\) None 0 8
8800.2.fz \(\chi_{8800}(1687, \cdot)\) None 0 8
8800.2.gk \(\chi_{8800}(823, \cdot)\) None 0 8
8800.2.gl \(\chi_{8800}(153, \cdot)\) None 0 8
8800.2.gm \(\chi_{8800}(457, \cdot)\) None 0 8
8800.2.gn \(\chi_{8800}(777, \cdot)\) None 0 8
8800.2.go \(\chi_{8800}(937, \cdot)\) None 0 8
8800.2.gp \(\chi_{8800}(983, \cdot)\) None 0 8
8800.2.gq \(\chi_{8800}(23, \cdot)\) None 0 8
8800.2.gr \(\chi_{8800}(807, \cdot)\) None 0 8
8800.2.gs \(\chi_{8800}(487, \cdot)\) None 0 8
8800.2.gt \(\chi_{8800}(953, \cdot)\) None 0 8
8800.2.gv \(\chi_{8800}(441, \cdot)\) None 0 8
8800.2.gw \(\chi_{8800}(791, \cdot)\) None 0 8
8800.2.gz \(\chi_{8800}(359, \cdot)\) None 0 8
8800.2.ha \(\chi_{8800}(1369, \cdot)\) None 0 8
8800.2.hc \(\chi_{8800}(9, \cdot)\) None 0 8
8800.2.he \(\chi_{8800}(1399, \cdot)\) None 0 8
8800.2.hh \(\chi_{8800}(3319, \cdot)\) None 0 8
8800.2.hi \(\chi_{8800}(519, \cdot)\) None 0 8
8800.2.hl \(\chi_{8800}(1609, \cdot)\) None 0 8
8800.2.hm \(\chi_{8800}(889, \cdot)\) None 0 8
8800.2.hp \(\chi_{8800}(1049, \cdot)\) None 0 8
8800.2.hr \(\chi_{8800}(39, \cdot)\) None 0 8
8800.2.ht \(\chi_{8800}(223, \cdot)\) n/a 2880 8
8800.2.hv \(\chi_{8800}(513, \cdot)\) n/a 2880 8
8800.2.hx \(\chi_{8800}(17, \cdot)\) n/a 2848 8
8800.2.hz \(\chi_{8800}(3887, \cdot)\) n/a 2848 8
8800.2.ia \(\chi_{8800}(1713, \cdot)\) n/a 2848 8
8800.2.ic \(\chi_{8800}(1423, \cdot)\) n/a 2848 8
8800.2.ie \(\chi_{8800}(193, \cdot)\) n/a 1728 8
8800.2.ig \(\chi_{8800}(863, \cdot)\) n/a 2880 8
8800.2.ii \(\chi_{8800}(287, \cdot)\) n/a 2400 8
8800.2.ij \(\chi_{8800}(1087, \cdot)\) n/a 2880 8
8800.2.im \(\chi_{8800}(417, \cdot)\) n/a 2880 8
8800.2.in \(\chi_{8800}(1217, \cdot)\) n/a 2880 8
8800.2.iq \(\chi_{8800}(673, \cdot)\) n/a 2880 8
8800.2.is \(\chi_{8800}(543, \cdot)\) n/a 1728 8
8800.2.iu \(\chi_{8800}(207, \cdot)\) n/a 1696 8
8800.2.iw \(\chi_{8800}(1297, \cdot)\) n/a 2848 8
8800.2.ix \(\chi_{8800}(1073, \cdot)\) n/a 2848 8
8800.2.ja \(\chi_{8800}(2097, \cdot)\) n/a 2848 8
8800.2.jc \(\chi_{8800}(687, \cdot)\) n/a 2848 8
8800.2.je \(\chi_{8800}(463, \cdot)\) n/a 2400 8
8800.2.jf \(\chi_{8800}(47, \cdot)\) n/a 2848 8
8800.2.ji \(\chi_{8800}(657, \cdot)\) n/a 1696 8
8800.2.jk \(\chi_{8800}(383, \cdot)\) n/a 2880 8
8800.2.jm \(\chi_{8800}(897, \cdot)\) n/a 2880 8
8800.2.jp \(\chi_{8800}(1961, \cdot)\) None 0 8
8800.2.jq \(\chi_{8800}(871, \cdot)\) None 0 8
8800.2.js \(\chi_{8800}(3671, \cdot)\) None 0 8
8800.2.ju \(\chi_{8800}(201, \cdot)\) None 0 8
8800.2.jx \(\chi_{8800}(1721, \cdot)\) None 0 8
8800.2.jy \(\chi_{8800}(361, \cdot)\) None 0 8
8800.2.kb \(\chi_{8800}(391, \cdot)\) None 0 8
8800.2.kc \(\chi_{8800}(711, \cdot)\) None 0 8
8800.2.kf \(\chi_{8800}(151, \cdot)\) None 0 8
8800.2.kh \(\chi_{8800}(1241, \cdot)\) None 0 8
8800.2.kj \(\chi_{8800}(439, \cdot)\) None 0 8
8800.2.kk \(\chi_{8800}(89, \cdot)\) None 0 8
8800.2.km \(\chi_{8800}(103, \cdot)\) None 0 8
8800.2.kn \(\chi_{8800}(1833, \cdot)\) None 0 8
8800.2.ko \(\chi_{8800}(1033, \cdot)\) None 0 8
8800.2.kp \(\chi_{8800}(73, \cdot)\) None 0 8
8800.2.kq \(\chi_{8800}(57, \cdot)\) None 0 8
8800.2.kr \(\chi_{8800}(727, \cdot)\) None 0 8
8800.2.ks \(\chi_{8800}(247, \cdot)\) None 0 8
8800.2.kt \(\chi_{8800}(1543, \cdot)\) None 0 8
8800.2.ku \(\chi_{8800}(423, \cdot)\) None 0 8
8800.2.kv \(\chi_{8800}(217, \cdot)\) None 0 8
8800.2.lg \(\chi_{8800}(633, \cdot)\) None 0 8
8800.2.lh \(\chi_{8800}(647, \cdot)\) None 0 8
8800.2.lk \(\chi_{8800}(373, \cdot)\) n/a 22976 16
8800.2.ln \(\chi_{8800}(67, \cdot)\) n/a 19200 16
8800.2.lo \(\chi_{8800}(893, \cdot)\) n/a 13760 16
8800.2.lq \(\chi_{8800}(267, \cdot)\) n/a 22976 16
8800.2.lu \(\chi_{8800}(3, \cdot)\) n/a 22976 16
8800.2.lv \(\chi_{8800}(587, \cdot)\) n/a 22976 16
8800.2.lw \(\chi_{8800}(323, \cdot)\) n/a 22976 16
8800.2.lz \(\chi_{8800}(13, \cdot)\) n/a 22976 16
8800.2.ma \(\chi_{8800}(173, \cdot)\) n/a 22976 16
8800.2.mb \(\chi_{8800}(437, \cdot)\) n/a 22976 16
8800.2.mf \(\chi_{8800}(277, \cdot)\) n/a 22976 16
8800.2.mh \(\chi_{8800}(643, \cdot)\) n/a 13760 16
8800.2.mj \(\chi_{8800}(141, \cdot)\) n/a 22976 16
8800.2.ml \(\chi_{8800}(1019, \cdot)\) n/a 22976 16
8800.2.mm \(\chi_{8800}(211, \cdot)\) n/a 22976 16
8800.2.mp \(\chi_{8800}(309, \cdot)\) n/a 19200 16
8800.2.mq \(\chi_{8800}(949, \cdot)\) n/a 13760 16
8800.2.mr \(\chi_{8800}(389, \cdot)\) n/a 22976 16
8800.2.mv \(\chi_{8800}(229, \cdot)\) n/a 22976 16
8800.2.mx \(\chi_{8800}(131, \cdot)\) n/a 22976 16
8800.2.my \(\chi_{8800}(171, \cdot)\) n/a 22976 16
8800.2.mz \(\chi_{8800}(51, \cdot)\) n/a 14496 16
8800.2.nd \(\chi_{8800}(491, \cdot)\) n/a 22976 16
8800.2.ne \(\chi_{8800}(69, \cdot)\) n/a 22976 16
8800.2.nh \(\chi_{8800}(19, \cdot)\) n/a 22976 16
8800.2.ni \(\chi_{8800}(181, \cdot)\) n/a 22976 16
8800.2.nm \(\chi_{8800}(221, \cdot)\) n/a 19200 16
8800.2.nn \(\chi_{8800}(301, \cdot)\) n/a 14496 16
8800.2.no \(\chi_{8800}(581, \cdot)\) n/a 22976 16
8800.2.nq \(\chi_{8800}(1179, \cdot)\) n/a 22976 16
8800.2.nu \(\chi_{8800}(219, \cdot)\) n/a 22976 16
8800.2.nv \(\chi_{8800}(139, \cdot)\) n/a 22976 16
8800.2.nw \(\chi_{8800}(299, \cdot)\) n/a 13760 16
8800.2.nz \(\chi_{8800}(1461, \cdot)\) n/a 22976 16
8800.2.oa \(\chi_{8800}(1109, \cdot)\) n/a 22976 16
8800.2.oc \(\chi_{8800}(371, \cdot)\) n/a 22976 16
8800.2.of \(\chi_{8800}(443, \cdot)\) n/a 13760 16
8800.2.oh \(\chi_{8800}(2213, \cdot)\) n/a 22976 16
8800.2.oi \(\chi_{8800}(453, \cdot)\) n/a 22976 16
8800.2.oj \(\chi_{8800}(613, \cdot)\) n/a 22976 16
8800.2.on \(\chi_{8800}(237, \cdot)\) n/a 22976 16
8800.2.oo \(\chi_{8800}(147, \cdot)\) n/a 22976 16
8800.2.os \(\chi_{8800}(2203, \cdot)\) n/a 22976 16
8800.2.ot \(\chi_{8800}(467, \cdot)\) n/a 22976 16
8800.2.ou \(\chi_{8800}(203, \cdot)\) n/a 22976 16
8800.2.ow \(\chi_{8800}(293, \cdot)\) n/a 13760 16
8800.2.oz \(\chi_{8800}(1123, \cdot)\) n/a 19200 16
8800.2.pa \(\chi_{8800}(197, \cdot)\) n/a 22976 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8800))\)\(^{\oplus 1}\)