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Properties

Label 39039.2
Level 39039
Weight 2
Dimension 38036544
Nonzero newspaces 240
Sturm bound 218050560

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Defining parameters

Level: \( N \) = \( 39039 = 3 \cdot 7 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 240 \)
Sturm bound: \(218050560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(39039))\).

Total New Old
Modular forms 54622080 38110160 16511920
Cusp forms 54403201 38036544 16366657
Eisenstein series 218879 73616 145263

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(39039))\)

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
39039.2.a \(\chi_{39039}(1, \cdot)\) 39039.2.a.a 1 1
39039.2.a.b 1
39039.2.a.c 1
39039.2.a.d 1
39039.2.a.e 1
39039.2.a.f 1
39039.2.a.g 1
39039.2.a.h 1
39039.2.a.i 1
39039.2.a.j 1
39039.2.a.k 1
39039.2.a.l 1
39039.2.a.m 1
39039.2.a.n 1
39039.2.a.o 1
39039.2.a.p 1
39039.2.a.q 1
39039.2.a.r 1
39039.2.a.s 1
39039.2.a.t 1
39039.2.a.u 1
39039.2.a.v 1
39039.2.a.w 1
39039.2.a.x 1
39039.2.a.y 1
39039.2.a.z 1
39039.2.a.ba 2
39039.2.a.bb 2
39039.2.a.bc 2
39039.2.a.bd 2
39039.2.a.be 3
39039.2.a.bf 3
39039.2.a.bg 3
39039.2.a.bh 3
39039.2.a.bi 5
39039.2.a.bj 5
39039.2.a.bk 5
39039.2.a.bl 5
39039.2.a.bm 6
39039.2.a.bn 6
39039.2.a.bo 6
39039.2.a.bp 6
39039.2.a.bq 7
39039.2.a.br 7
39039.2.a.bs 8
39039.2.a.bt 8
39039.2.a.bu 9
39039.2.a.bv 9
39039.2.a.bw 9
39039.2.a.bx 11
39039.2.a.by 12
39039.2.a.bz 12
39039.2.a.ca 13
39039.2.a.cb 13
39039.2.a.cc 14
39039.2.a.cd 14
39039.2.a.ce 14
39039.2.a.cf 14
39039.2.a.cg 14
39039.2.a.ch 14
39039.2.a.ci 14
39039.2.a.cj 14
39039.2.a.ck 15
39039.2.a.cl 15
39039.2.a.cm 19
39039.2.a.cn 19
39039.2.a.co 21
39039.2.a.cp 21
39039.2.a.cq 21
39039.2.a.cr 21
39039.2.a.cs 21
39039.2.a.ct 21
39039.2.a.cu 21
39039.2.a.cv 21
39039.2.a.cw 28
39039.2.a.cx 28
39039.2.a.cy 28
39039.2.a.cz 28
39039.2.a.da 40
39039.2.a.db 40
39039.2.a.dc 40
39039.2.a.dd 40
39039.2.a.de 45
39039.2.a.df 45
39039.2.a.dg 45
39039.2.a.dh 45
39039.2.a.di 45
39039.2.a.dj 45
39039.2.a.dk 45
39039.2.a.dl 45
39039.2.a.dm 45
39039.2.a.dn 45
39039.2.a.do 45
39039.2.a.dp 45
39039.2.a.dq 45
39039.2.a.dr 45
39039.2.a.ds 45
39039.2.a.dt 45
39039.2.d \(\chi_{39039}(25180, \cdot)\) n/a 1544 1
39039.2.e \(\chi_{39039}(26872, \cdot)\) n/a 2480 1
39039.2.h \(\chi_{39039}(31604, \cdot)\) n/a 4132 1
39039.2.i \(\chi_{39039}(33461, \cdot)\) n/a 3696 1
39039.2.l \(\chi_{39039}(8282, \cdot)\) n/a 3720 1
39039.2.m \(\chi_{39039}(17744, \cdot)\) n/a 4104 1
39039.2.p \(\chi_{39039}(13012, \cdot)\) n/a 2464 1
39039.2.q \(\chi_{39039}(11155, \cdot)\) n/a 4132 2
39039.2.r \(\chi_{39039}(991, \cdot)\) n/a 4108 2
39039.2.s \(\chi_{39039}(28414, \cdot)\) n/a 3072 2
39039.2.t \(\chi_{39039}(529, \cdot)\) n/a 4108 2
39039.2.w \(\chi_{39039}(2465, \cdot)\) n/a 6160 2
39039.2.x \(\chi_{39039}(23561, \cdot)\) n/a 9776 2
39039.2.ba \(\chi_{39039}(30997, \cdot)\) n/a 3696 2
39039.2.bb \(\chi_{39039}(15280, \cdot)\) n/a 4112 2
39039.2.bc \(\chi_{39039}(7099, \cdot)\) n/a 7440 4
39039.2.bf \(\chi_{39039}(16202, \cdot)\) n/a 9776 2
39039.2.bg \(\chi_{39039}(4709, \cdot)\) n/a 8212 2
39039.2.bj \(\chi_{39039}(5092, \cdot)\) n/a 4928 2
39039.2.bk \(\chi_{39039}(7921, \cdot)\) n/a 4108 2
39039.2.bl \(\chi_{39039}(27908, \cdot)\) n/a 8216 2
39039.2.bm \(\chi_{39039}(36695, \cdot)\) n/a 7392 2
39039.2.bp \(\chi_{39039}(1858, \cdot)\) n/a 4928 2
39039.2.bs \(\chi_{39039}(6907, \cdot)\) n/a 4928 2
39039.2.bv \(\chi_{39039}(9272, \cdot)\) n/a 9776 2
39039.2.bw \(\chi_{39039}(11639, \cdot)\) n/a 8212 2
39039.2.bz \(\chi_{39039}(1013, \cdot)\) n/a 8216 2
39039.2.ca \(\chi_{39039}(19436, \cdot)\) n/a 9832 2
39039.2.cd \(\chi_{39039}(23176, \cdot)\) n/a 4928 2
39039.2.cg \(\chi_{39039}(16246, \cdot)\) n/a 4928 2
39039.2.ch \(\chi_{39039}(35344, \cdot)\) n/a 3088 2
39039.2.ck \(\chi_{39039}(4247, \cdot)\) n/a 8212 2
39039.2.cl \(\chi_{39039}(15740, \cdot)\) n/a 9776 2
39039.2.co \(\chi_{39039}(5576, \cdot)\) n/a 9776 2
39039.2.cp \(\chi_{39039}(14873, \cdot)\) n/a 8268 2
39039.2.cs \(\chi_{39039}(10141, \cdot)\) n/a 4960 2
39039.2.ct \(\chi_{39039}(2872, \cdot)\) n/a 4104 2
39039.2.cw \(\chi_{39039}(7459, \cdot)\) n/a 4108 2
39039.2.cx \(\chi_{39039}(5554, \cdot)\) n/a 4928 2
39039.2.da \(\chi_{39039}(4586, \cdot)\) n/a 7392 2
39039.2.db \(\chi_{39039}(20978, \cdot)\) n/a 8216 2
39039.2.dg \(\chi_{39039}(6445, \cdot)\) n/a 4928 2
39039.2.dj \(\chi_{39039}(11177, \cdot)\) n/a 8212 2
39039.2.dk \(\chi_{39039}(8810, \cdot)\) n/a 9776 2
39039.2.dl \(\chi_{39039}(5914, \cdot)\) n/a 9856 4
39039.2.do \(\chi_{39039}(10646, \cdot)\) n/a 19552 4
39039.2.dp \(\chi_{39039}(1184, \cdot)\) n/a 14880 4
39039.2.ds \(\chi_{39039}(1520, \cdot)\) n/a 14784 4
39039.2.dt \(\chi_{39039}(10310, \cdot)\) n/a 19664 4
39039.2.dw \(\chi_{39039}(9127, \cdot)\) n/a 9920 4
39039.2.dx \(\chi_{39039}(3886, \cdot)\) n/a 7392 4
39039.2.ec \(\chi_{39039}(2047, \cdot)\) n/a 8216 4
39039.2.ed \(\chi_{39039}(1033, \cdot)\) n/a 9856 4
39039.2.eg \(\chi_{39039}(10328, \cdot)\) n/a 19552 4
39039.2.eh \(\chi_{39039}(4643, \cdot)\) n/a 16424 4
39039.2.ei \(\chi_{39039}(3629, \cdot)\) n/a 19552 4
39039.2.ej \(\chi_{39039}(11342, \cdot)\) n/a 16424 4
39039.2.em \(\chi_{39039}(6502, \cdot)\) n/a 8208 4
39039.2.en \(\chi_{39039}(6511, \cdot)\) n/a 7392 4
39039.2.eo \(\chi_{39039}(3112, \cdot)\) n/a 9856 4
39039.2.ep \(\chi_{39039}(4126, \cdot)\) n/a 8208 4
39039.2.eu \(\chi_{39039}(14783, \cdot)\) n/a 19552 4
39039.2.ev \(\chi_{39039}(4544, \cdot)\) n/a 12320 4
39039.2.ew \(\chi_{39039}(7844, \cdot)\) n/a 16432 4
39039.2.ex \(\chi_{39039}(6830, \cdot)\) n/a 19552 4
39039.2.fc \(\chi_{39039}(6403, \cdot)\) n/a 8216 4
39039.2.fd \(\chi_{39039}(6610, \cdot)\) n/a 9856 4
39039.2.fg \(\chi_{39039}(3004, \cdot)\) n/a 21888 12
39039.2.fh \(\chi_{39039}(3019, \cdot)\) n/a 19712 8
39039.2.fi \(\chi_{39039}(7120, \cdot)\) n/a 14784 8
39039.2.fj \(\chi_{39039}(4057, \cdot)\) n/a 19840 8
39039.2.fk \(\chi_{39039}(2557, \cdot)\) n/a 19712 8
39039.2.fl \(\chi_{39039}(5816, \cdot)\) n/a 39104 8
39039.2.fm \(\chi_{39039}(3788, \cdot)\) n/a 29568 8
39039.2.fp \(\chi_{39039}(8182, \cdot)\) n/a 19712 8
39039.2.fq \(\chi_{39039}(1282, \cdot)\) n/a 14784 8
39039.2.ft \(\chi_{39039}(1000, \cdot)\) n/a 34944 12
39039.2.fw \(\chi_{39039}(2276, \cdot)\) n/a 52416 12
39039.2.fx \(\chi_{39039}(2729, \cdot)\) n/a 58272 12
39039.2.ga \(\chi_{39039}(1574, \cdot)\) n/a 58272 12
39039.2.gb \(\chi_{39039}(428, \cdot)\) n/a 52416 12
39039.2.ge \(\chi_{39039}(1156, \cdot)\) n/a 21792 12
39039.2.gf \(\chi_{39039}(2848, \cdot)\) n/a 34944 12
39039.2.gi \(\chi_{39039}(1712, \cdot)\) n/a 39104 8
39039.2.gj \(\chi_{39039}(4079, \cdot)\) n/a 39104 8
39039.2.gm \(\chi_{39039}(5386, \cdot)\) n/a 19712 8
39039.2.gr \(\chi_{39039}(146, \cdot)\) n/a 39104 8
39039.2.gs \(\chi_{39039}(8135, \cdot)\) n/a 29568 8
39039.2.gv \(\chi_{39039}(4393, \cdot)\) n/a 19712 8
39039.2.gw \(\chi_{39039}(3043, \cdot)\) n/a 19840 8
39039.2.gz \(\chi_{39039}(3064, \cdot)\) n/a 19712 8
39039.2.ha \(\chi_{39039}(361, \cdot)\) n/a 19712 8
39039.2.hd \(\chi_{39039}(4034, \cdot)\) n/a 39104 8
39039.2.he \(\chi_{39039}(698, \cdot)\) n/a 39104 8
39039.2.hh \(\chi_{39039}(7775, \cdot)\) n/a 39328 8
39039.2.hi \(\chi_{39039}(4055, \cdot)\) n/a 39104 8
39039.2.hl \(\chi_{39039}(3403, \cdot)\) n/a 14784 8
39039.2.hm \(\chi_{39039}(9148, \cdot)\) n/a 19712 8
39039.2.hp \(\chi_{39039}(5431, \cdot)\) n/a 19712 8
39039.2.hs \(\chi_{39039}(4541, \cdot)\) n/a 39104 8
39039.2.ht \(\chi_{39039}(2174, \cdot)\) n/a 39104 8
39039.2.hw \(\chi_{39039}(1691, \cdot)\) n/a 39328 8
39039.2.hx \(\chi_{39039}(3041, \cdot)\) n/a 39104 8
39039.2.ia \(\chi_{39039}(3379, \cdot)\) n/a 19712 8
39039.2.id \(\chi_{39039}(4924, \cdot)\) n/a 19712 8
39039.2.ig \(\chi_{39039}(1205, \cdot)\) n/a 29568 8
39039.2.ih \(\chi_{39039}(6614, \cdot)\) n/a 39104 8
39039.2.ii \(\chi_{39039}(823, \cdot)\) n/a 19712 8
39039.2.ij \(\chi_{39039}(3526, \cdot)\) n/a 19712 8
39039.2.im \(\chi_{39039}(1160, \cdot)\) n/a 39104 8
39039.2.in \(\chi_{39039}(3572, \cdot)\) n/a 39104 8
39039.2.iq \(\chi_{39039}(562, \cdot)\) n/a 58224 24
39039.2.ir \(\chi_{39039}(1387, \cdot)\) n/a 43776 24
39039.2.is \(\chi_{39039}(100, \cdot)\) n/a 58224 24
39039.2.it \(\chi_{39039}(1717, \cdot)\) n/a 58272 24
39039.2.iu \(\chi_{39039}(34, \cdot)\) n/a 58176 24
39039.2.iv \(\chi_{39039}(736, \cdot)\) n/a 52416 24
39039.2.iy \(\chi_{39039}(2309, \cdot)\) n/a 139584 24
39039.2.iz \(\chi_{39039}(2696, \cdot)\) n/a 87360 24
39039.2.je \(\chi_{39039}(1103, \cdot)\) n/a 78208 16
39039.2.jf \(\chi_{39039}(7178, \cdot)\) n/a 78208 16
39039.2.jk \(\chi_{39039}(577, \cdot)\) n/a 39424 16
39039.2.jl \(\chi_{39039}(1591, \cdot)\) n/a 39424 16
39039.2.jm \(\chi_{39039}(3361, \cdot)\) n/a 29568 16
39039.2.jn \(\chi_{39039}(1840, \cdot)\) n/a 39424 16
39039.2.js \(\chi_{39039}(437, \cdot)\) n/a 78208 16
39039.2.jt \(\chi_{39039}(746, \cdot)\) n/a 78208 16
39039.2.ju \(\chi_{39039}(995, \cdot)\) n/a 59136 16
39039.2.jv \(\chi_{39039}(2624, \cdot)\) n/a 78208 16
39039.2.jy \(\chi_{39039}(1432, \cdot)\) n/a 39424 16
39039.2.jz \(\chi_{39039}(2446, \cdot)\) n/a 39424 16
39039.2.ka \(\chi_{39039}(3460, \cdot)\) n/a 39424 16
39039.2.kb \(\chi_{39039}(4882, \cdot)\) n/a 39424 16
39039.2.ke \(\chi_{39039}(1094, \cdot)\) n/a 78208 16
39039.2.kf \(\chi_{39039}(1601, \cdot)\) n/a 78208 16
39039.2.ki \(\chi_{39039}(1093, \cdot)\) n/a 104832 48
39039.2.kj \(\chi_{39039}(2168, \cdot)\) n/a 116496 24
39039.2.kk \(\chi_{39039}(2804, \cdot)\) n/a 139584 24
39039.2.kn \(\chi_{39039}(439, \cdot)\) n/a 69888 24
39039.2.ks \(\chi_{39039}(1583, \cdot)\) n/a 104832 24
39039.2.kt \(\chi_{39039}(419, \cdot)\) n/a 116448 24
39039.2.kw \(\chi_{39039}(1453, \cdot)\) n/a 58224 24
39039.2.kx \(\chi_{39039}(2518, \cdot)\) n/a 69888 24
39039.2.la \(\chi_{39039}(703, \cdot)\) n/a 69888 24
39039.2.lb \(\chi_{39039}(298, \cdot)\) n/a 58272 24
39039.2.le \(\chi_{39039}(2144, \cdot)\) n/a 139584 24
39039.2.lf \(\chi_{39039}(2432, \cdot)\) n/a 116448 24
39039.2.li \(\chi_{39039}(1244, \cdot)\) n/a 116496 24
39039.2.lj \(\chi_{39039}(725, \cdot)\) n/a 139584 24
39039.2.lm \(\chi_{39039}(1231, \cdot)\) n/a 69888 24
39039.2.ln \(\chi_{39039}(2311, \cdot)\) n/a 43584 24
39039.2.lq \(\chi_{39039}(2155, \cdot)\) n/a 69888 24
39039.2.lt \(\chi_{39039}(584, \cdot)\) n/a 116448 24
39039.2.lu \(\chi_{39039}(989, \cdot)\) n/a 139584 24
39039.2.lx \(\chi_{39039}(263, \cdot)\) n/a 139584 24
39039.2.ly \(\chi_{39039}(1739, \cdot)\) n/a 116496 24
39039.2.mb \(\chi_{39039}(10, \cdot)\) n/a 69888 24
39039.2.me \(\chi_{39039}(2287, \cdot)\) n/a 69888 24
39039.2.mh \(\chi_{39039}(881, \cdot)\) n/a 116448 24
39039.2.mi \(\chi_{39039}(659, \cdot)\) n/a 104832 24
39039.2.mj \(\chi_{39039}(2089, \cdot)\) n/a 69888 24
39039.2.mk \(\chi_{39039}(1024, \cdot)\) n/a 58224 24
39039.2.mn \(\chi_{39039}(296, \cdot)\) n/a 139584 24
39039.2.mo \(\chi_{39039}(815, \cdot)\) n/a 116496 24
39039.2.mt \(\chi_{39039}(118, \cdot)\) n/a 139776 48
39039.2.mu \(\chi_{39039}(64, \cdot)\) n/a 104832 48
39039.2.mx \(\chi_{39039}(701, \cdot)\) n/a 209664 48
39039.2.my \(\chi_{39039}(482, \cdot)\) n/a 279168 48
39039.2.nb \(\chi_{39039}(818, \cdot)\) n/a 279168 48
39039.2.nc \(\chi_{39039}(365, \cdot)\) n/a 209664 48
39039.2.nf \(\chi_{39039}(1273, \cdot)\) n/a 139776 48
39039.2.ni \(\chi_{39039}(340, \cdot)\) n/a 139776 48
39039.2.nj \(\chi_{39039}(397, \cdot)\) n/a 116448 48
39039.2.no \(\chi_{39039}(164, \cdot)\) n/a 279168 48
39039.2.np \(\chi_{39039}(1178, \cdot)\) n/a 232896 48
39039.2.nq \(\chi_{39039}(617, \cdot)\) n/a 174720 48
39039.2.nr \(\chi_{39039}(461, \cdot)\) n/a 279168 48
39039.2.nw \(\chi_{39039}(892, \cdot)\) n/a 116544 48
39039.2.nx \(\chi_{39039}(109, \cdot)\) n/a 139776 48
39039.2.ny \(\chi_{39039}(505, \cdot)\) n/a 104832 48
39039.2.nz \(\chi_{39039}(496, \cdot)\) n/a 116544 48
39039.2.oc \(\chi_{39039}(254, \cdot)\) n/a 232992 48
39039.2.od \(\chi_{39039}(626, \cdot)\) n/a 279168 48
39039.2.oe \(\chi_{39039}(683, \cdot)\) n/a 232992 48
39039.2.of \(\chi_{39039}(362, \cdot)\) n/a 279168 48
39039.2.oi \(\chi_{39039}(1957, \cdot)\) n/a 139776 48
39039.2.oj \(\chi_{39039}(1090, \cdot)\) n/a 116448 48
39039.2.om \(\chi_{39039}(445, \cdot)\) n/a 279552 96
39039.2.on \(\chi_{39039}(235, \cdot)\) n/a 279552 96
39039.2.oo \(\chi_{39039}(295, \cdot)\) n/a 209664 96
39039.2.op \(\chi_{39039}(16, \cdot)\) n/a 279552 96
39039.2.os \(\chi_{39039}(1009, \cdot)\) n/a 209664 96
39039.2.ot \(\chi_{39039}(1126, \cdot)\) n/a 279552 96
39039.2.ow \(\chi_{39039}(554, \cdot)\) n/a 419328 96
39039.2.ox \(\chi_{39039}(83, \cdot)\) n/a 558336 96
39039.2.pa \(\chi_{39039}(269, \cdot)\) n/a 558336 96
39039.2.pb \(\chi_{39039}(95, \cdot)\) n/a 558336 96
39039.2.pe \(\chi_{39039}(4, \cdot)\) n/a 279552 96
39039.2.pf \(\chi_{39039}(178, \cdot)\) n/a 279552 96
39039.2.pg \(\chi_{39039}(29, \cdot)\) n/a 419328 96
39039.2.ph \(\chi_{39039}(251, \cdot)\) n/a 558336 96
39039.2.pk \(\chi_{39039}(283, \cdot)\) n/a 279552 96
39039.2.pn \(\chi_{39039}(376, \cdot)\) n/a 279552 96
39039.2.pq \(\chi_{39039}(326, \cdot)\) n/a 558336 96
39039.2.pr \(\chi_{39039}(38, \cdot)\) n/a 558336 96
39039.2.pu \(\chi_{39039}(647, \cdot)\) n/a 558336 96
39039.2.pv \(\chi_{39039}(464, \cdot)\) n/a 558336 96
39039.2.py \(\chi_{39039}(160, \cdot)\) n/a 279552 96
39039.2.qb \(\chi_{39039}(400, \cdot)\) n/a 209664 96
39039.2.qc \(\chi_{39039}(139, \cdot)\) n/a 279552 96
39039.2.qf \(\chi_{39039}(521, \cdot)\) n/a 558336 96
39039.2.qg \(\chi_{39039}(116, \cdot)\) n/a 558336 96
39039.2.qj \(\chi_{39039}(998, \cdot)\) n/a 558336 96
39039.2.qk \(\chi_{39039}(152, \cdot)\) n/a 558336 96
39039.2.qn \(\chi_{39039}(61, \cdot)\) n/a 279552 96
39039.2.qo \(\chi_{39039}(394, \cdot)\) n/a 279552 96
39039.2.qr \(\chi_{39039}(25, \cdot)\) n/a 279552 96
39039.2.qs \(\chi_{39039}(40, \cdot)\) n/a 279552 96
39039.2.qv \(\chi_{39039}(1049, \cdot)\) n/a 558336 96
39039.2.qw \(\chi_{39039}(134, \cdot)\) n/a 419328 96
39039.2.rb \(\chi_{39039}(712, \cdot)\) n/a 279552 96
39039.2.re \(\chi_{39039}(74, \cdot)\) n/a 558336 96
39039.2.rf \(\chi_{39039}(257, \cdot)\) n/a 558336 96
39039.2.ri \(\chi_{39039}(227, \cdot)\) n/a 1116672 192
39039.2.rj \(\chi_{39039}(137, \cdot)\) n/a 1116672 192
39039.2.rm \(\chi_{39039}(136, \cdot)\) n/a 559104 192
39039.2.rn \(\chi_{39039}(46, \cdot)\) n/a 559104 192
39039.2.ro \(\chi_{39039}(115, \cdot)\) n/a 559104 192
39039.2.rp \(\chi_{39039}(193, \cdot)\) n/a 559104 192
39039.2.rs \(\chi_{39039}(41, \cdot)\) n/a 1116672 192
39039.2.rt \(\chi_{39039}(71, \cdot)\) n/a 838656 192
39039.2.ru \(\chi_{39039}(86, \cdot)\) n/a 1116672 192
39039.2.rv \(\chi_{39039}(668, \cdot)\) n/a 1116672 192
39039.2.sa \(\chi_{39039}(97, \cdot)\) n/a 559104 192
39039.2.sb \(\chi_{39039}(85, \cdot)\) n/a 419328 192
39039.2.sc \(\chi_{39039}(151, \cdot)\) n/a 559104 192
39039.2.sd \(\chi_{39039}(31, \cdot)\) n/a 559104 192
39039.2.si \(\chi_{39039}(206, \cdot)\) n/a 1116672 192
39039.2.sj \(\chi_{39039}(158, \cdot)\) n/a 1116672 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(39039))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(39039)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1001))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1859))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3003))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3549))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5577))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13013))\)\(^{\oplus 2}\)