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Properties

Label 31734.2
Level 31734
Weight 2
Dimension 7356770
Nonzero newspaces 160
Sturm bound 111767040

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Defining parameters

Level: \( N \) = \( 31734 = 2 \cdot 3^{2} \cdot 41 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 160 \)
Sturm bound: \(111767040\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(31734))\).

Total New Old
Modular forms 27995520 7356770 20638750
Cusp forms 27888001 7356770 20531231
Eisenstein series 107519 0 107519

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(31734))\)

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
31734.2.a \(\chi_{31734}(1, \cdot)\) 31734.2.a.a 1 1
31734.2.a.b 1
31734.2.a.c 1
31734.2.a.d 1
31734.2.a.e 1
31734.2.a.f 1
31734.2.a.g 1
31734.2.a.h 1
31734.2.a.i 1
31734.2.a.j 1
31734.2.a.k 1
31734.2.a.l 1
31734.2.a.m 1
31734.2.a.n 1
31734.2.a.o 1
31734.2.a.p 1
31734.2.a.q 2
31734.2.a.r 2
31734.2.a.s 2
31734.2.a.t 3
31734.2.a.u 4
31734.2.a.v 9
31734.2.a.w 11
31734.2.a.x 12
31734.2.a.y 12
31734.2.a.z 12
31734.2.a.ba 12
31734.2.a.bb 13
31734.2.a.bc 13
31734.2.a.bd 14
31734.2.a.be 16
31734.2.a.bf 16
31734.2.a.bg 17
31734.2.a.bh 17
31734.2.a.bi 17
31734.2.a.bj 17
31734.2.a.bk 18
31734.2.a.bl 18
31734.2.a.bm 20
31734.2.a.bn 20
31734.2.a.bo 20
31734.2.a.bp 21
31734.2.a.bq 22
31734.2.a.br 22
31734.2.a.bs 24
31734.2.a.bt 29
31734.2.a.bu 29
31734.2.a.bv 29
31734.2.a.bw 29
31734.2.a.bx 40
31734.2.a.by 40
31734.2.a.bz 41
31734.2.a.ca 41
31734.2.f \(\chi_{31734}(19351, \cdot)\) n/a 734 1
31734.2.g \(\chi_{31734}(12383, \cdot)\) n/a 592 1
31734.2.h \(\chi_{31734}(31733, \cdot)\) n/a 616 1
31734.2.i \(\chi_{31734}(10579, \cdot)\) n/a 3360 2
31734.2.j \(\chi_{31734}(20173, \cdot)\) n/a 3520 2
31734.2.k \(\chi_{31734}(3691, \cdot)\) n/a 1464 2
31734.2.l \(\chi_{31734}(14269, \cdot)\) n/a 3520 2
31734.2.m \(\chi_{31734}(13931, \cdot)\) n/a 1232 2
31734.2.n \(\chi_{31734}(1549, \cdot)\) n/a 1472 2
31734.2.q \(\chi_{31734}(775, \cdot)\) n/a 2936 4
31734.2.v \(\chi_{31734}(6887, \cdot)\) n/a 3696 2
31734.2.w \(\chi_{31734}(10577, \cdot)\) n/a 3696 2
31734.2.x \(\chi_{31734}(22139, \cdot)\) n/a 1232 2
31734.2.y \(\chi_{31734}(2789, \cdot)\) n/a 1168 2
31734.2.z \(\chi_{31734}(23041, \cdot)\) n/a 1540 2
31734.2.ba \(\chi_{31734}(7789, \cdot)\) n/a 3696 2
31734.2.bb \(\chi_{31734}(1805, \cdot)\) n/a 3520 2
31734.2.bc \(\chi_{31734}(8773, \cdot)\) n/a 3528 2
31734.2.bd \(\chi_{31734}(19271, \cdot)\) n/a 3520 2
31734.2.bq \(\chi_{31734}(13367, \cdot)\) n/a 3520 2
31734.2.br \(\chi_{31734}(1885, \cdot)\) n/a 3696 2
31734.2.bs \(\chi_{31734}(983, \cdot)\) n/a 3696 2
31734.2.bt \(\chi_{31734}(6643, \cdot)\) n/a 4416 6
31734.2.bu \(\chi_{31734}(11179, \cdot)\) n/a 3080 4
31734.2.bx \(\chi_{31734}(5849, \cdot)\) n/a 2352 4
31734.2.by \(\chi_{31734}(2321, \cdot)\) n/a 2464 4
31734.2.bz \(\chi_{31734}(4643, \cdot)\) n/a 2464 4
31734.2.ca \(\chi_{31734}(9289, \cdot)\) n/a 2936 4
31734.2.cf \(\chi_{31734}(14915, \cdot)\) n/a 7392 4
31734.2.cg \(\chi_{31734}(337, \cdot)\) n/a 7392 4
31734.2.cn \(\chi_{31734}(6241, \cdot)\) n/a 7392 4
31734.2.co \(\chi_{31734}(5239, \cdot)\) n/a 3080 4
31734.2.cp \(\chi_{31734}(7225, \cdot)\) n/a 7056 4
31734.2.cq \(\chi_{31734}(3353, \cdot)\) n/a 7392 4
31734.2.cr \(\chi_{31734}(4337, \cdot)\) n/a 2464 4
31734.2.cs \(\chi_{31734}(5339, \cdot)\) n/a 7392 4
31734.2.cv \(\chi_{31734}(4265, \cdot)\) n/a 3552 6
31734.2.cw \(\chi_{31734}(901, \cdot)\) n/a 4620 6
31734.2.cx \(\chi_{31734}(2951, \cdot)\) n/a 3696 6
31734.2.dc \(\chi_{31734}(6529, \cdot)\) n/a 14784 8
31734.2.dd \(\chi_{31734}(1369, \cdot)\) n/a 6160 8
31734.2.de \(\chi_{31734}(3175, \cdot)\) n/a 14784 8
31734.2.df \(\chi_{31734}(2839, \cdot)\) n/a 14112 8
31734.2.di \(\chi_{31734}(6193, \cdot)\) n/a 5888 8
31734.2.dj \(\chi_{31734}(3095, \cdot)\) n/a 4928 8
31734.2.dk \(\chi_{31734}(3199, \cdot)\) n/a 21120 12
31734.2.dl \(\chi_{31734}(1477, \cdot)\) n/a 8784 12
31734.2.dm \(\chi_{31734}(2461, \cdot)\) n/a 21120 12
31734.2.dn \(\chi_{31734}(2707, \cdot)\) n/a 21120 12
31734.2.dp \(\chi_{31734}(1039, \cdot)\) n/a 14784 8
31734.2.dr \(\chi_{31734}(9539, \cdot)\) n/a 4928 8
31734.2.ds \(\chi_{31734}(3089, \cdot)\) n/a 14784 8
31734.2.dv \(\chi_{31734}(5333, \cdot)\) n/a 14112 8
31734.2.dw \(\chi_{31734}(85, \cdot)\) n/a 14784 8
31734.2.dz \(\chi_{31734}(1555, \cdot)\) n/a 14784 8
31734.2.ea \(\chi_{31734}(1585, \cdot)\) n/a 6160 8
31734.2.ec \(\chi_{31734}(3605, \cdot)\) n/a 14784 8
31734.2.eg \(\chi_{31734}(4519, \cdot)\) n/a 9240 12
31734.2.eh \(\chi_{31734}(647, \cdot)\) n/a 7392 12
31734.2.ei \(\chi_{31734}(209, \cdot)\) n/a 14784 8
31734.2.ej \(\chi_{31734}(1111, \cdot)\) n/a 14784 8
31734.2.ek \(\chi_{31734}(5627, \cdot)\) n/a 14784 8
31734.2.ex \(\chi_{31734}(2273, \cdot)\) n/a 14784 8
31734.2.ey \(\chi_{31734}(517, \cdot)\) n/a 14112 8
31734.2.ez \(\chi_{31734}(1289, \cdot)\) n/a 14784 8
31734.2.fa \(\chi_{31734}(2401, \cdot)\) n/a 14784 8
31734.2.fb \(\chi_{31734}(4951, \cdot)\) n/a 6160 8
31734.2.fc \(\chi_{31734}(467, \cdot)\) n/a 4928 8
31734.2.fd \(\chi_{31734}(4049, \cdot)\) n/a 4928 8
31734.2.fe \(\chi_{31734}(515, \cdot)\) n/a 14784 8
31734.2.ff \(\chi_{31734}(1499, \cdot)\) n/a 14784 8
31734.2.fk \(\chi_{31734}(379, \cdot)\) n/a 18480 24
31734.2.fl \(\chi_{31734}(1979, \cdot)\) n/a 9408 16
31734.2.fo \(\chi_{31734}(343, \cdot)\) n/a 12320 16
31734.2.fp \(\chi_{31734}(655, \cdot)\) n/a 22176 12
31734.2.fq \(\chi_{31734}(329, \cdot)\) n/a 21120 12
31734.2.fr \(\chi_{31734}(491, \cdot)\) n/a 22176 12
31734.2.ge \(\chi_{31734}(2213, \cdot)\) n/a 7392 12
31734.2.gf \(\chi_{31734}(1967, \cdot)\) n/a 22176 12
31734.2.gg \(\chi_{31734}(245, \cdot)\) n/a 22176 12
31734.2.gh \(\chi_{31734}(2297, \cdot)\) n/a 21120 12
31734.2.gi \(\chi_{31734}(4837, \cdot)\) n/a 22176 12
31734.2.gj \(\chi_{31734}(3773, \cdot)\) n/a 21120 12
31734.2.gk \(\chi_{31734}(1393, \cdot)\) n/a 22176 12
31734.2.gl \(\chi_{31734}(5329, \cdot)\) n/a 9240 12
31734.2.gm \(\chi_{31734}(2051, \cdot)\) n/a 7008 12
31734.2.gs \(\chi_{31734}(2105, \cdot)\) n/a 14784 24
31734.2.gt \(\chi_{31734}(2053, \cdot)\) n/a 18480 24
31734.2.gx \(\chi_{31734}(695, \cdot)\) n/a 29568 16
31734.2.gy \(\chi_{31734}(1727, \cdot)\) n/a 9856 16
31734.2.gz \(\chi_{31734}(2837, \cdot)\) n/a 29568 16
31734.2.ha \(\chi_{31734}(1033, \cdot)\) n/a 28224 16
31734.2.hb \(\chi_{31734}(307, \cdot)\) n/a 12320 16
31734.2.hc \(\chi_{31734}(49, \cdot)\) n/a 29568 16
31734.2.hj \(\chi_{31734}(4981, \cdot)\) n/a 29568 16
31734.2.hk \(\chi_{31734}(4079, \cdot)\) n/a 29568 16
31734.2.hp \(\chi_{31734}(1097, \cdot)\) n/a 14784 24
31734.2.hq \(\chi_{31734}(127, \cdot)\) n/a 18480 24
31734.2.hr \(\chi_{31734}(1943, \cdot)\) n/a 14784 24
31734.2.hu \(\chi_{31734}(419, \cdot)\) n/a 44352 24
31734.2.hv \(\chi_{31734}(155, \cdot)\) n/a 44352 24
31734.2.hw \(\chi_{31734}(665, \cdot)\) n/a 14784 24
31734.2.hx \(\chi_{31734}(3025, \cdot)\) n/a 18480 24
31734.2.hy \(\chi_{31734}(1303, \cdot)\) n/a 44352 24
31734.2.hz \(\chi_{31734}(3289, \cdot)\) n/a 44352 24
31734.2.ig \(\chi_{31734}(583, \cdot)\) n/a 44352 24
31734.2.ih \(\chi_{31734}(893, \cdot)\) n/a 44352 24
31734.2.ii \(\chi_{31734}(133, \cdot)\) n/a 88704 48
31734.2.ij \(\chi_{31734}(139, \cdot)\) n/a 88704 48
31734.2.ik \(\chi_{31734}(1945, \cdot)\) n/a 36960 48
31734.2.il \(\chi_{31734}(283, \cdot)\) n/a 88704 48
31734.2.in \(\chi_{31734}(479, \cdot)\) n/a 59136 32
31734.2.ip \(\chi_{31734}(1297, \cdot)\) n/a 24640 32
31734.2.iq \(\chi_{31734}(7, \cdot)\) n/a 59136 32
31734.2.it \(\chi_{31734}(1375, \cdot)\) n/a 59136 32
31734.2.iu \(\chi_{31734}(1463, \cdot)\) n/a 56448 32
31734.2.ix \(\chi_{31734}(767, \cdot)\) n/a 59136 32
31734.2.iy \(\chi_{31734}(1511, \cdot)\) n/a 19712 32
31734.2.ja \(\chi_{31734}(265, \cdot)\) n/a 59136 32
31734.2.jc \(\chi_{31734}(125, \cdot)\) n/a 29568 48
31734.2.jd \(\chi_{31734}(613, \cdot)\) n/a 36960 48
31734.2.jg \(\chi_{31734}(1175, \cdot)\) n/a 88704 48
31734.2.ji \(\chi_{31734}(2023, \cdot)\) n/a 88704 48
31734.2.jl \(\chi_{31734}(55, \cdot)\) n/a 36960 48
31734.2.jm \(\chi_{31734}(331, \cdot)\) n/a 88704 48
31734.2.jp \(\chi_{31734}(167, \cdot)\) n/a 88704 48
31734.2.jq \(\chi_{31734}(683, \cdot)\) n/a 29568 48
31734.2.jt \(\chi_{31734}(1397, \cdot)\) n/a 88704 48
31734.2.jv \(\chi_{31734}(1093, \cdot)\) n/a 88704 48
31734.2.ka \(\chi_{31734}(1781, \cdot)\) n/a 29568 48
31734.2.kb \(\chi_{31734}(271, \cdot)\) n/a 36960 48
31734.2.kc \(\chi_{31734}(25, \cdot)\) n/a 88704 48
31734.2.kd \(\chi_{31734}(1451, \cdot)\) n/a 88704 48
31734.2.ke \(\chi_{31734}(1417, \cdot)\) n/a 88704 48
31734.2.kf \(\chi_{31734}(707, \cdot)\) n/a 88704 48
31734.2.kg \(\chi_{31734}(2327, \cdot)\) n/a 88704 48
31734.2.kh \(\chi_{31734}(113, \cdot)\) n/a 88704 48
31734.2.ki \(\chi_{31734}(845, \cdot)\) n/a 29568 48
31734.2.kv \(\chi_{31734}(605, \cdot)\) n/a 88704 48
31734.2.kw \(\chi_{31734}(119, \cdot)\) n/a 88704 48
31734.2.kx \(\chi_{31734}(1357, \cdot)\) n/a 88704 48
31734.2.kz \(\chi_{31734}(199, \cdot)\) n/a 73920 96
31734.2.la \(\chi_{31734}(35, \cdot)\) n/a 59136 96
31734.2.lc \(\chi_{31734}(77, \cdot)\) n/a 177408 96
31734.2.ld \(\chi_{31734}(103, \cdot)\) n/a 177408 96
31734.2.lk \(\chi_{31734}(121, \cdot)\) n/a 177408 96
31734.2.ll \(\chi_{31734}(799, \cdot)\) n/a 177408 96
31734.2.lm \(\chi_{31734}(289, \cdot)\) n/a 73920 96
31734.2.ln \(\chi_{31734}(377, \cdot)\) n/a 59136 96
31734.2.lo \(\chi_{31734}(5, \cdot)\) n/a 177408 96
31734.2.lp \(\chi_{31734}(131, \cdot)\) n/a 177408 96
31734.2.ls \(\chi_{31734}(157, \cdot)\) n/a 354816 192
31734.2.lu \(\chi_{31734}(11, \cdot)\) n/a 354816 192
31734.2.lx \(\chi_{31734}(17, \cdot)\) n/a 118272 192
31734.2.ly \(\chi_{31734}(101, \cdot)\) n/a 354816 192
31734.2.mb \(\chi_{31734}(175, \cdot)\) n/a 354816 192
31734.2.mc \(\chi_{31734}(19, \cdot)\) n/a 147840 192
31734.2.mf \(\chi_{31734}(151, \cdot)\) n/a 354816 192
31734.2.mh \(\chi_{31734}(95, \cdot)\) n/a 354816 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(31734))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(31734)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(258))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(369))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(387))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(738))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(774))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1763))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3526))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15867))\)\(^{\oplus 2}\)