↑

Properties

Label 27885.2
Level 27885
Weight 2
Dimension 18186912
Nonzero newspaces 160
Sturm bound 109025280

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 27885 = 3 \cdot 5 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 160 \)
Sturm bound: \(109025280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(27885))\).

Total New Old
Modular forms 27329280 18231080 9098200
Cusp forms 27183361 18186912 8996449
Eisenstein series 145919 44168 101751

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(27885))\)

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
27885.2.a \(\chi_{27885}(1, \cdot)\) 27885.2.a.a 1 1
27885.2.a.b 1
27885.2.a.c 1
27885.2.a.d 1
27885.2.a.e 1
27885.2.a.f 1
27885.2.a.g 1
27885.2.a.h 1
27885.2.a.i 1
27885.2.a.j 1
27885.2.a.k 1
27885.2.a.l 1
27885.2.a.m 1
27885.2.a.n 1
27885.2.a.o 1
27885.2.a.p 1
27885.2.a.q 1
27885.2.a.r 1
27885.2.a.s 1
27885.2.a.t 1
27885.2.a.u 1
27885.2.a.v 1
27885.2.a.w 1
27885.2.a.x 1
27885.2.a.y 2
27885.2.a.z 2
27885.2.a.ba 2
27885.2.a.bb 2
27885.2.a.bc 2
27885.2.a.bd 2
27885.2.a.be 2
27885.2.a.bf 2
27885.2.a.bg 3
27885.2.a.bh 3
27885.2.a.bi 3
27885.2.a.bj 3
27885.2.a.bk 3
27885.2.a.bl 3
27885.2.a.bm 3
27885.2.a.bn 3
27885.2.a.bo 3
27885.2.a.bp 4
27885.2.a.bq 4
27885.2.a.br 4
27885.2.a.bs 4
27885.2.a.bt 4
27885.2.a.bu 4
27885.2.a.bv 4
27885.2.a.bw 4
27885.2.a.bx 4
27885.2.a.by 4
27885.2.a.bz 4
27885.2.a.ca 5
27885.2.a.cb 5
27885.2.a.cc 5
27885.2.a.cd 5
27885.2.a.ce 5
27885.2.a.cf 6
27885.2.a.cg 6
27885.2.a.ch 6
27885.2.a.ci 6
27885.2.a.cj 6
27885.2.a.ck 6
27885.2.a.cl 7
27885.2.a.cm 7
27885.2.a.cn 8
27885.2.a.co 8
27885.2.a.cp 9
27885.2.a.cq 9
27885.2.a.cr 9
27885.2.a.cs 9
27885.2.a.ct 9
27885.2.a.cu 9
27885.2.a.cv 10
27885.2.a.cw 10
27885.2.a.cx 13
27885.2.a.cy 13
27885.2.a.cz 14
27885.2.a.da 14
27885.2.a.db 14
27885.2.a.dc 14
27885.2.a.dd 15
27885.2.a.de 15
27885.2.a.df 15
27885.2.a.dg 15
27885.2.a.dh 22
27885.2.a.di 22
27885.2.a.dj 24
27885.2.a.dk 24
27885.2.a.dl 24
27885.2.a.dm 24
27885.2.a.dn 24
27885.2.a.do 24
27885.2.a.dp 26
27885.2.a.dq 26
27885.2.a.dr 28
27885.2.a.ds 28
27885.2.a.dt 30
27885.2.a.du 30
27885.2.a.dv 30
27885.2.a.dw 30
27885.2.a.dx 30
27885.2.a.dy 30
27885.2.a.dz 33
27885.2.a.ea 33
27885.2.a.eb 36
27885.2.a.ec 36
27885.2.c \(\chi_{27885}(22309, \cdot)\) n/a 1548 1
27885.2.d \(\chi_{27885}(14026, \cdot)\) n/a 1024 1
27885.2.f \(\chi_{27885}(13859, \cdot)\) n/a 3676 1
27885.2.i \(\chi_{27885}(5576, \cdot)\) n/a 2464 1
27885.2.k \(\chi_{27885}(27884, \cdot)\) n/a 3656 1
27885.2.l \(\chi_{27885}(19436, \cdot)\) n/a 2480 1
27885.2.n \(\chi_{27885}(8449, \cdot)\) n/a 1544 1
27885.2.q \(\chi_{27885}(991, \cdot)\) n/a 2056 2
27885.2.r \(\chi_{27885}(1253, \cdot)\) n/a 7312 2
27885.2.t \(\chi_{27885}(9703, \cdot)\) n/a 3080 2
27885.2.v \(\chi_{27885}(7844, \cdot)\) n/a 6160 2
27885.2.y \(\chi_{27885}(1858, \cdot)\) n/a 3696 2
27885.2.ba \(\chi_{27885}(15718, \cdot)\) n/a 3720 2
27885.2.bc \(\chi_{27885}(13421, \cdot)\) n/a 4112 2
27885.2.be \(\chi_{27885}(8689, \cdot)\) n/a 3696 2
27885.2.bg \(\chi_{27885}(14873, \cdot)\) n/a 6200 2
27885.2.bi \(\chi_{27885}(1013, \cdot)\) n/a 6160 2
27885.2.bj \(\chi_{27885}(14266, \cdot)\) n/a 2464 2
27885.2.bl \(\chi_{27885}(15478, \cdot)\) n/a 3080 2
27885.2.bn \(\chi_{27885}(7028, \cdot)\) n/a 7312 2
27885.2.bp \(\chi_{27885}(7606, \cdot)\) n/a 4960 4
27885.2.bs \(\chi_{27885}(2344, \cdot)\) n/a 3088 2
27885.2.bu \(\chi_{27885}(20426, \cdot)\) n/a 4928 2
27885.2.bv \(\chi_{27885}(21779, \cdot)\) n/a 7312 2
27885.2.bx \(\chi_{27885}(4586, \cdot)\) n/a 4928 2
27885.2.ca \(\chi_{27885}(14849, \cdot)\) n/a 7312 2
27885.2.cc \(\chi_{27885}(7921, \cdot)\) n/a 2056 2
27885.2.cd \(\chi_{27885}(529, \cdot)\) n/a 3072 2
27885.2.ch \(\chi_{27885}(16054, \cdot)\) n/a 7392 4
27885.2.cj \(\chi_{27885}(1691, \cdot)\) n/a 9920 4
27885.2.ck \(\chi_{27885}(10139, \cdot)\) n/a 14624 4
27885.2.cm \(\chi_{27885}(15716, \cdot)\) n/a 9856 4
27885.2.cp \(\chi_{27885}(1184, \cdot)\) n/a 14704 4
27885.2.cr \(\chi_{27885}(1351, \cdot)\) n/a 4928 4
27885.2.cs \(\chi_{27885}(2029, \cdot)\) n/a 7440 4
27885.2.cv \(\chi_{27885}(21383, \cdot)\) n/a 14624 4
27885.2.cx \(\chi_{27885}(1948, \cdot)\) n/a 6160 4
27885.2.cy \(\chi_{27885}(5666, \cdot)\) n/a 8208 4
27885.2.da \(\chi_{27885}(5092, \cdot)\) n/a 7392 4
27885.2.dc \(\chi_{27885}(868, \cdot)\) n/a 7392 4
27885.2.df \(\chi_{27885}(89, \cdot)\) n/a 12320 4
27885.2.dh \(\chi_{27885}(6511, \cdot)\) n/a 4928 4
27885.2.di \(\chi_{27885}(23, \cdot)\) n/a 12320 4
27885.2.dk \(\chi_{27885}(4247, \cdot)\) n/a 12320 4
27885.2.dm \(\chi_{27885}(934, \cdot)\) n/a 7392 4
27885.2.dp \(\chi_{27885}(13102, \cdot)\) n/a 6160 4
27885.2.dr \(\chi_{27885}(4652, \cdot)\) n/a 14624 4
27885.2.ds \(\chi_{27885}(2146, \cdot)\) n/a 14592 12
27885.2.dt \(\chi_{27885}(8596, \cdot)\) n/a 9856 8
27885.2.dv \(\chi_{27885}(4802, \cdot)\) n/a 29248 8
27885.2.dx \(\chi_{27885}(268, \cdot)\) n/a 14784 8
27885.2.dy \(\chi_{27885}(1591, \cdot)\) n/a 9856 8
27885.2.ea \(\chi_{27885}(2027, \cdot)\) n/a 29248 8
27885.2.ec \(\chi_{27885}(2198, \cdot)\) n/a 29408 8
27885.2.ef \(\chi_{27885}(1084, \cdot)\) n/a 14784 8
27885.2.eh \(\chi_{27885}(746, \cdot)\) n/a 19712 8
27885.2.ei \(\chi_{27885}(508, \cdot)\) n/a 14880 8
27885.2.ek \(\chi_{27885}(337, \cdot)\) n/a 14784 8
27885.2.em \(\chi_{27885}(944, \cdot)\) n/a 29248 8
27885.2.ep \(\chi_{27885}(6352, \cdot)\) n/a 14784 8
27885.2.er \(\chi_{27885}(437, \cdot)\) n/a 29248 8
27885.2.et \(\chi_{27885}(2014, \cdot)\) n/a 21792 12
27885.2.ev \(\chi_{27885}(131, \cdot)\) n/a 34944 12
27885.2.ey \(\chi_{27885}(2144, \cdot)\) n/a 52320 12
27885.2.fa \(\chi_{27885}(1286, \cdot)\) n/a 34944 12
27885.2.fb \(\chi_{27885}(989, \cdot)\) n/a 52320 12
27885.2.fd \(\chi_{27885}(1156, \cdot)\) n/a 14592 12
27885.2.fg \(\chi_{27885}(859, \cdot)\) n/a 21888 12
27885.2.fi \(\chi_{27885}(3019, \cdot)\) n/a 14784 8
27885.2.fj \(\chi_{27885}(361, \cdot)\) n/a 9856 8
27885.2.fl \(\chi_{27885}(2174, \cdot)\) n/a 29248 8
27885.2.fo \(\chi_{27885}(9611, \cdot)\) n/a 19712 8
27885.2.fq \(\chi_{27885}(4034, \cdot)\) n/a 29248 8
27885.2.fr \(\chi_{27885}(2681, \cdot)\) n/a 19712 8
27885.2.ft \(\chi_{27885}(9949, \cdot)\) n/a 14784 8
27885.2.fw \(\chi_{27885}(1816, \cdot)\) n/a 29088 24
27885.2.fy \(\chi_{27885}(593, \cdot)\) n/a 104640 24
27885.2.ga \(\chi_{27885}(463, \cdot)\) n/a 43680 24
27885.2.gb \(\chi_{27885}(736, \cdot)\) n/a 34944 24
27885.2.gd \(\chi_{27885}(287, \cdot)\) n/a 87360 24
27885.2.gf \(\chi_{27885}(1442, \cdot)\) n/a 87360 24
27885.2.gi \(\chi_{27885}(109, \cdot)\) n/a 52416 24
27885.2.gk \(\chi_{27885}(551, \cdot)\) n/a 58176 24
27885.2.gl \(\chi_{27885}(142, \cdot)\) n/a 52416 24
27885.2.gn \(\chi_{27885}(703, \cdot)\) n/a 52416 24
27885.2.gp \(\chi_{27885}(749, \cdot)\) n/a 87360 24
27885.2.gs \(\chi_{27885}(892, \cdot)\) n/a 43680 24
27885.2.gu \(\chi_{27885}(1022, \cdot)\) n/a 104640 24
27885.2.gv \(\chi_{27885}(1502, \cdot)\) n/a 58496 16
27885.2.gx \(\chi_{27885}(427, \cdot)\) n/a 29568 16
27885.2.gz \(\chi_{27885}(19, \cdot)\) n/a 29568 16
27885.2.hc \(\chi_{27885}(653, \cdot)\) n/a 58496 16
27885.2.he \(\chi_{27885}(1037, \cdot)\) n/a 58496 16
27885.2.hg \(\chi_{27885}(3361, \cdot)\) n/a 19712 16
27885.2.hi \(\chi_{27885}(1094, \cdot)\) n/a 58496 16
27885.2.hk \(\chi_{27885}(4417, \cdot)\) n/a 29568 16
27885.2.hm \(\chi_{27885}(1498, \cdot)\) n/a 29568 16
27885.2.hn \(\chi_{27885}(2216, \cdot)\) n/a 39424 16
27885.2.hp \(\chi_{27885}(9553, \cdot)\) n/a 29568 16
27885.2.hr \(\chi_{27885}(3638, \cdot)\) n/a 58496 16
27885.2.ht \(\chi_{27885}(196, \cdot)\) n/a 69888 48
27885.2.hu \(\chi_{27885}(1849, \cdot)\) n/a 43776 24
27885.2.hx \(\chi_{27885}(166, \cdot)\) n/a 29088 24
27885.2.hz \(\chi_{27885}(659, \cdot)\) n/a 104640 24
27885.2.ia \(\chi_{27885}(296, \cdot)\) n/a 69888 24
27885.2.ic \(\chi_{27885}(329, \cdot)\) n/a 104640 24
27885.2.if \(\chi_{27885}(1121, \cdot)\) n/a 69888 24
27885.2.ih \(\chi_{27885}(199, \cdot)\) n/a 43584 24
27885.2.ij \(\chi_{27885}(664, \cdot)\) n/a 104832 48
27885.2.im \(\chi_{27885}(181, \cdot)\) n/a 69888 48
27885.2.io \(\chi_{27885}(404, \cdot)\) n/a 209280 48
27885.2.ip \(\chi_{27885}(116, \cdot)\) n/a 139776 48
27885.2.ir \(\chi_{27885}(194, \cdot)\) n/a 209280 48
27885.2.iu \(\chi_{27885}(326, \cdot)\) n/a 139776 48
27885.2.iw \(\chi_{27885}(64, \cdot)\) n/a 104832 48
27885.2.iy \(\chi_{27885}(362, \cdot)\) n/a 209280 48
27885.2.ja \(\chi_{27885}(232, \cdot)\) n/a 87360 48
27885.2.jc \(\chi_{27885}(604, \cdot)\) n/a 104832 48
27885.2.jf \(\chi_{27885}(452, \cdot)\) n/a 174720 48
27885.2.jh \(\chi_{27885}(848, \cdot)\) n/a 174720 48
27885.2.jj \(\chi_{27885}(76, \cdot)\) n/a 69888 48
27885.2.jl \(\chi_{27885}(254, \cdot)\) n/a 174720 48
27885.2.jn \(\chi_{27885}(373, \cdot)\) n/a 104832 48
27885.2.jp \(\chi_{27885}(43, \cdot)\) n/a 104832 48
27885.2.jq \(\chi_{27885}(1046, \cdot)\) n/a 116544 48
27885.2.js \(\chi_{27885}(67, \cdot)\) n/a 87360 48
27885.2.ju \(\chi_{27885}(32, \cdot)\) n/a 209280 48
27885.2.jw \(\chi_{27885}(16, \cdot)\) n/a 139776 96
27885.2.jx \(\chi_{27885}(83, \cdot)\) n/a 418560 96
27885.2.jz \(\chi_{27885}(148, \cdot)\) n/a 209664 96
27885.2.kb \(\chi_{27885}(434, \cdot)\) n/a 418560 96
27885.2.ke \(\chi_{27885}(118, \cdot)\) n/a 209664 96
27885.2.kg \(\chi_{27885}(688, \cdot)\) n/a 209664 96
27885.2.ki \(\chi_{27885}(86, \cdot)\) n/a 279552 96
27885.2.kk \(\chi_{27885}(304, \cdot)\) n/a 209664 96
27885.2.km \(\chi_{27885}(38, \cdot)\) n/a 418560 96
27885.2.ko \(\chi_{27885}(53, \cdot)\) n/a 418560 96
27885.2.kp \(\chi_{27885}(151, \cdot)\) n/a 139776 96
27885.2.kr \(\chi_{27885}(658, \cdot)\) n/a 209664 96
27885.2.kt \(\chi_{27885}(8, \cdot)\) n/a 418560 96
27885.2.kw \(\chi_{27885}(4, \cdot)\) n/a 209664 96
27885.2.ky \(\chi_{27885}(536, \cdot)\) n/a 279552 96
27885.2.lb \(\chi_{27885}(134, \cdot)\) n/a 418560 96
27885.2.ld \(\chi_{27885}(101, \cdot)\) n/a 279552 96
27885.2.le \(\chi_{27885}(29, \cdot)\) n/a 418560 96
27885.2.lg \(\chi_{27885}(511, \cdot)\) n/a 139776 96
27885.2.lj \(\chi_{27885}(289, \cdot)\) n/a 209664 96
27885.2.ll \(\chi_{27885}(2, \cdot)\) n/a 837120 192
27885.2.ln \(\chi_{27885}(97, \cdot)\) n/a 419328 192
27885.2.lo \(\chi_{27885}(71, \cdot)\) n/a 559104 192
27885.2.lq \(\chi_{27885}(127, \cdot)\) n/a 419328 192
27885.2.ls \(\chi_{27885}(172, \cdot)\) n/a 419328 192
27885.2.lv \(\chi_{27885}(59, \cdot)\) n/a 837120 192
27885.2.lx \(\chi_{27885}(46, \cdot)\) n/a 279552 192
27885.2.ly \(\chi_{27885}(113, \cdot)\) n/a 837120 192
27885.2.ma \(\chi_{27885}(212, \cdot)\) n/a 837120 192
27885.2.mc \(\chi_{27885}(184, \cdot)\) n/a 419328 192
27885.2.mf \(\chi_{27885}(37, \cdot)\) n/a 419328 192
27885.2.mh \(\chi_{27885}(167, \cdot)\) n/a 837120 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(27885))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(27885)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(715))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1859))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2535))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5577))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9295))\)\(^{\oplus 2}\)