Properties

Label 6039.2
Level 6039
Weight 2
Dimension 1037190
Nonzero newspaces 210
Sturm bound 5356800

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Defining parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 210 \)
Sturm bound: \(5356800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6039))\).

Total New Old
Modular forms 1348800 1046750 302050
Cusp forms 1329601 1037190 292411
Eisenstein series 19199 9560 9639

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6039))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6039.2.a \(\chi_{6039}(1, \cdot)\) 6039.2.a.a 5 1
6039.2.a.b 6
6039.2.a.c 11
6039.2.a.d 11
6039.2.a.e 12
6039.2.a.f 12
6039.2.a.g 13
6039.2.a.h 13
6039.2.a.i 13
6039.2.a.j 14
6039.2.a.k 19
6039.2.a.l 21
6039.2.a.m 25
6039.2.a.n 25
6039.2.a.o 25
6039.2.a.p 25
6039.2.b \(\chi_{6039}(6038, \cdot)\) n/a 248 1
6039.2.e \(\chi_{6039}(1585, \cdot)\) n/a 256 1
6039.2.f \(\chi_{6039}(4454, \cdot)\) n/a 240 1
6039.2.i \(\chi_{6039}(2575, \cdot)\) n/a 520 2
6039.2.j \(\chi_{6039}(2014, \cdot)\) n/a 1200 2
6039.2.k \(\chi_{6039}(3829, \cdot)\) n/a 1240 2
6039.2.l \(\chi_{6039}(562, \cdot)\) n/a 1240 2
6039.2.m \(\chi_{6039}(4564, \cdot)\) n/a 616 2
6039.2.p \(\chi_{6039}(782, \cdot)\) n/a 408 2
6039.2.q \(\chi_{6039}(874, \cdot)\) n/a 1232 4
6039.2.r \(\chi_{6039}(3070, \cdot)\) n/a 1032 4
6039.2.s \(\chi_{6039}(1648, \cdot)\) n/a 1200 4
6039.2.t \(\chi_{6039}(1351, \cdot)\) n/a 1232 4
6039.2.u \(\chi_{6039}(1522, \cdot)\) n/a 1232 4
6039.2.v \(\chi_{6039}(973, \cdot)\) n/a 1232 4
6039.2.w \(\chi_{6039}(3037, \cdot)\) n/a 1240 2
6039.2.z \(\chi_{6039}(4223, \cdot)\) n/a 1480 2
6039.2.ba \(\chi_{6039}(230, \cdot)\) n/a 1480 2
6039.2.bf \(\chi_{6039}(428, \cdot)\) n/a 1440 2
6039.2.bh \(\chi_{6039}(989, \cdot)\) n/a 496 2
6039.2.bj \(\chi_{6039}(1451, \cdot)\) n/a 1480 2
6039.2.bl \(\chi_{6039}(3598, \cdot)\) n/a 1240 2
6039.2.bn \(\chi_{6039}(1783, \cdot)\) n/a 516 2
6039.2.bq \(\chi_{6039}(197, \cdot)\) n/a 496 2
6039.2.bs \(\chi_{6039}(2012, \cdot)\) n/a 1480 2
6039.2.bu \(\chi_{6039}(1024, \cdot)\) n/a 1240 2
6039.2.bx \(\chi_{6039}(2243, \cdot)\) n/a 1480 2
6039.2.by \(\chi_{6039}(163, \cdot)\) n/a 1232 4
6039.2.cb \(\chi_{6039}(1322, \cdot)\) n/a 992 4
6039.2.cd \(\chi_{6039}(314, \cdot)\) n/a 992 4
6039.2.cj \(\chi_{6039}(2510, \cdot)\) n/a 992 4
6039.2.cl \(\chi_{6039}(62, \cdot)\) n/a 960 4
6039.2.cm \(\chi_{6039}(1484, \cdot)\) n/a 992 4
6039.2.co \(\chi_{6039}(3572, \cdot)\) n/a 992 4
6039.2.cs \(\chi_{6039}(332, \cdot)\) n/a 992 4
6039.2.ct \(\chi_{6039}(1369, \cdot)\) n/a 1232 4
6039.2.cv \(\chi_{6039}(487, \cdot)\) n/a 1232 4
6039.2.cy \(\chi_{6039}(64, \cdot)\) n/a 1232 4
6039.2.da \(\chi_{6039}(1882, \cdot)\) n/a 1024 4
6039.2.db \(\chi_{6039}(296, \cdot)\) n/a 992 4
6039.2.dd \(\chi_{6039}(1223, \cdot)\) n/a 992 4
6039.2.dg \(\chi_{6039}(1097, \cdot)\) n/a 992 4
6039.2.di \(\chi_{6039}(3968, \cdot)\) n/a 992 4
6039.2.dj \(\chi_{6039}(2809, \cdot)\) n/a 1232 4
6039.2.dn \(\chi_{6039}(3779, \cdot)\) n/a 992 4
6039.2.do \(\chi_{6039}(947, \cdot)\) n/a 2480 4
6039.2.dr \(\chi_{6039}(1363, \cdot)\) n/a 2960 4
6039.2.ds \(\chi_{6039}(1066, \cdot)\) n/a 2960 4
6039.2.du \(\chi_{6039}(2795, \cdot)\) n/a 2480 4
6039.2.dv \(\chi_{6039}(2663, \cdot)\) n/a 832 4
6039.2.ea \(\chi_{6039}(406, \cdot)\) n/a 1232 4
6039.2.eb \(\chi_{6039}(538, \cdot)\) n/a 2960 4
6039.2.ed \(\chi_{6039}(650, \cdot)\) n/a 2480 4
6039.2.ee \(\chi_{6039}(850, \cdot)\) n/a 5920 8
6039.2.ef \(\chi_{6039}(400, \cdot)\) n/a 5920 8
6039.2.eg \(\chi_{6039}(757, \cdot)\) n/a 2464 8
6039.2.eh \(\chi_{6039}(25, \cdot)\) n/a 5920 8
6039.2.ei \(\chi_{6039}(169, \cdot)\) n/a 5920 8
6039.2.ej \(\chi_{6039}(1123, \cdot)\) n/a 4960 8
6039.2.ek \(\chi_{6039}(1093, \cdot)\) n/a 5920 8
6039.2.el \(\chi_{6039}(1582, \cdot)\) n/a 5920 8
6039.2.em \(\chi_{6039}(1534, \cdot)\) n/a 5920 8
6039.2.en \(\chi_{6039}(1765, \cdot)\) n/a 2464 8
6039.2.eo \(\chi_{6039}(565, \cdot)\) n/a 5920 8
6039.2.ep \(\chi_{6039}(196, \cdot)\) n/a 5920 8
6039.2.eq \(\chi_{6039}(16, \cdot)\) n/a 5920 8
6039.2.er \(\chi_{6039}(727, \cdot)\) n/a 4960 8
6039.2.es \(\chi_{6039}(58, \cdot)\) n/a 5920 8
6039.2.et \(\chi_{6039}(361, \cdot)\) n/a 2464 8
6039.2.eu \(\chi_{6039}(379, \cdot)\) n/a 2464 8
6039.2.ev \(\chi_{6039}(34, \cdot)\) n/a 4960 8
6039.2.ew \(\chi_{6039}(70, \cdot)\) n/a 5920 8
6039.2.ex \(\chi_{6039}(199, \cdot)\) n/a 2080 8
6039.2.ey \(\chi_{6039}(2269, \cdot)\) n/a 2464 8
6039.2.ez \(\chi_{6039}(367, \cdot)\) n/a 5760 8
6039.2.fa \(\chi_{6039}(103, \cdot)\) n/a 5920 8
6039.2.fb \(\chi_{6039}(1642, \cdot)\) n/a 5920 8
6039.2.fc \(\chi_{6039}(647, \cdot)\) n/a 1984 8
6039.2.ff \(\chi_{6039}(28, \cdot)\) n/a 2464 8
6039.2.fh \(\chi_{6039}(541, \cdot)\) n/a 2464 8
6039.2.fj \(\chi_{6039}(1070, \cdot)\) n/a 1984 8
6039.2.fk \(\chi_{6039}(1061, \cdot)\) n/a 1984 8
6039.2.fl \(\chi_{6039}(377, \cdot)\) n/a 1984 8
6039.2.fp \(\chi_{6039}(89, \cdot)\) n/a 1632 8
6039.2.fq \(\chi_{6039}(1000, \cdot)\) n/a 2464 8
6039.2.fu \(\chi_{6039}(172, \cdot)\) n/a 2464 8
6039.2.fv \(\chi_{6039}(2224, \cdot)\) n/a 2464 8
6039.2.fw \(\chi_{6039}(145, \cdot)\) n/a 2464 8
6039.2.fy \(\chi_{6039}(53, \cdot)\) n/a 1984 8
6039.2.ga \(\chi_{6039}(167, \cdot)\) n/a 5920 8
6039.2.gd \(\chi_{6039}(97, \cdot)\) n/a 5920 8
6039.2.gf \(\chi_{6039}(1052, \cdot)\) n/a 1984 8
6039.2.gh \(\chi_{6039}(95, \cdot)\) n/a 5920 8
6039.2.gm \(\chi_{6039}(83, \cdot)\) n/a 5920 8
6039.2.go \(\chi_{6039}(1262, \cdot)\) n/a 5920 8
6039.2.gr \(\chi_{6039}(266, \cdot)\) n/a 5920 8
6039.2.gt \(\chi_{6039}(164, \cdot)\) n/a 5920 8
6039.2.gu \(\chi_{6039}(596, \cdot)\) n/a 5920 8
6039.2.ha \(\chi_{6039}(1337, \cdot)\) n/a 5920 8
6039.2.hd \(\chi_{6039}(248, \cdot)\) n/a 5920 8
6039.2.hf \(\chi_{6039}(289, \cdot)\) n/a 2464 8
6039.2.hh \(\chi_{6039}(796, \cdot)\) n/a 5920 8
6039.2.hj \(\chi_{6039}(4, \cdot)\) n/a 5920 8
6039.2.hl \(\chi_{6039}(463, \cdot)\) n/a 4960 8
6039.2.hm \(\chi_{6039}(1417, \cdot)\) n/a 5920 8
6039.2.ho \(\chi_{6039}(49, \cdot)\) n/a 5920 8
6039.2.hq \(\chi_{6039}(149, \cdot)\) n/a 5920 8
6039.2.hs \(\chi_{6039}(431, \cdot)\) n/a 1984 8
6039.2.hu \(\chi_{6039}(1295, \cdot)\) n/a 1984 8
6039.2.hx \(\chi_{6039}(1064, \cdot)\) n/a 5920 8
6039.2.hz \(\chi_{6039}(857, \cdot)\) n/a 5920 8
6039.2.ib \(\chi_{6039}(107, \cdot)\) n/a 1984 8
6039.2.id \(\chi_{6039}(890, \cdot)\) n/a 1984 8
6039.2.ie \(\chi_{6039}(182, \cdot)\) n/a 5920 8
6039.2.ih \(\chi_{6039}(1219, \cdot)\) n/a 5920 8
6039.2.ii \(\chi_{6039}(100, \cdot)\) n/a 2064 8
6039.2.ik \(\chi_{6039}(280, \cdot)\) n/a 2464 8
6039.2.im \(\chi_{6039}(430, \cdot)\) n/a 4960 8
6039.2.io \(\chi_{6039}(346, \cdot)\) n/a 5920 8
6039.2.ir \(\chi_{6039}(136, \cdot)\) n/a 2464 8
6039.2.it \(\chi_{6039}(829, \cdot)\) n/a 2464 8
6039.2.iv \(\chi_{6039}(895, \cdot)\) n/a 5920 8
6039.2.ix \(\chi_{6039}(842, \cdot)\) n/a 5920 8
6039.2.iz \(\chi_{6039}(563, \cdot)\) n/a 5920 8
6039.2.ja \(\chi_{6039}(2540, \cdot)\) n/a 5920 8
6039.2.jc \(\chi_{6039}(893, \cdot)\) n/a 5920 8
6039.2.je \(\chi_{6039}(41, \cdot)\) n/a 5920 8
6039.2.jg \(\chi_{6039}(161, \cdot)\) n/a 1984 8
6039.2.ji \(\chi_{6039}(202, \cdot)\) n/a 5920 8
6039.2.jl \(\chi_{6039}(545, \cdot)\) n/a 5920 8
6039.2.js \(\chi_{6039}(794, \cdot)\) n/a 5760 8
6039.2.jv \(\chi_{6039}(503, \cdot)\) n/a 1984 8
6039.2.jx \(\chi_{6039}(1781, \cdot)\) n/a 1984 8
6039.2.jz \(\chi_{6039}(1559, \cdot)\) n/a 5920 8
6039.2.kb \(\chi_{6039}(131, \cdot)\) n/a 5920 8
6039.2.kc \(\chi_{6039}(413, \cdot)\) n/a 1984 8
6039.2.ke \(\chi_{6039}(260, \cdot)\) n/a 1984 8
6039.2.kg \(\chi_{6039}(497, \cdot)\) n/a 5920 8
6039.2.kq \(\chi_{6039}(1154, \cdot)\) n/a 5920 8
6039.2.ks \(\chi_{6039}(1733, \cdot)\) n/a 5920 8
6039.2.kv \(\chi_{6039}(74, \cdot)\) n/a 5920 8
6039.2.kx \(\chi_{6039}(1184, \cdot)\) n/a 5920 8
6039.2.ky \(\chi_{6039}(134, \cdot)\) n/a 1984 8
6039.2.la \(\chi_{6039}(569, \cdot)\) n/a 5920 8
6039.2.le \(\chi_{6039}(229, \cdot)\) n/a 5920 8
6039.2.lf \(\chi_{6039}(380, \cdot)\) n/a 5920 8
6039.2.li \(\chi_{6039}(1073, \cdot)\) n/a 5920 8
6039.2.lk \(\chi_{6039}(65, \cdot)\) n/a 5920 8
6039.2.ll \(\chi_{6039}(524, \cdot)\) n/a 5920 8
6039.2.lo \(\chi_{6039}(1285, \cdot)\) n/a 5920 8
6039.2.lp \(\chi_{6039}(232, \cdot)\) n/a 4960 8
6039.2.lr \(\chi_{6039}(1483, \cdot)\) n/a 5920 8
6039.2.lu \(\chi_{6039}(841, \cdot)\) n/a 5920 8
6039.2.lv \(\chi_{6039}(1910, \cdot)\) n/a 5920 8
6039.2.lx \(\chi_{6039}(553, \cdot)\) n/a 5920 8
6039.2.lz \(\chi_{6039}(1040, \cdot)\) n/a 5920 8
6039.2.mb \(\chi_{6039}(656, \cdot)\) n/a 1984 8
6039.2.me \(\chi_{6039}(1666, \cdot)\) n/a 2464 8
6039.2.mg \(\chi_{6039}(247, \cdot)\) n/a 5920 8
6039.2.mi \(\chi_{6039}(293, \cdot)\) n/a 5920 8
6039.2.mj \(\chi_{6039}(239, \cdot)\) n/a 5920 8
6039.2.mm \(\chi_{6039}(349, \cdot)\) n/a 11840 16
6039.2.mp \(\chi_{6039}(311, \cdot)\) n/a 11840 16
6039.2.mr \(\chi_{6039}(79, \cdot)\) n/a 11840 16
6039.2.mu \(\chi_{6039}(26, \cdot)\) n/a 3968 16
6039.2.mv \(\chi_{6039}(38, \cdot)\) n/a 11840 16
6039.2.mx \(\chi_{6039}(212, \cdot)\) n/a 11840 16
6039.2.my \(\chi_{6039}(434, \cdot)\) n/a 11840 16
6039.2.mz \(\chi_{6039}(383, \cdot)\) n/a 11840 16
6039.2.nd \(\chi_{6039}(518, \cdot)\) n/a 9920 16
6039.2.ng \(\chi_{6039}(226, \cdot)\) n/a 4928 16
6039.2.nh \(\chi_{6039}(211, \cdot)\) n/a 11840 16
6039.2.ni \(\chi_{6039}(904, \cdot)\) n/a 11840 16
6039.2.nj \(\chi_{6039}(1432, \cdot)\) n/a 4928 16
6039.2.nk \(\chi_{6039}(811, \cdot)\) n/a 4928 16
6039.2.nl \(\chi_{6039}(358, \cdot)\) n/a 11840 16
6039.2.ns \(\chi_{6039}(175, \cdot)\) n/a 11840 16
6039.2.nt \(\chi_{6039}(10, \cdot)\) n/a 4928 16
6039.2.nu \(\chi_{6039}(287, \cdot)\) n/a 3328 16
6039.2.nv \(\chi_{6039}(23, \cdot)\) n/a 9920 16
6039.2.oc \(\chi_{6039}(236, \cdot)\) n/a 11840 16
6039.2.od \(\chi_{6039}(872, \cdot)\) n/a 3968 16
6039.2.oe \(\chi_{6039}(467, \cdot)\) n/a 3968 16
6039.2.of \(\chi_{6039}(416, \cdot)\) n/a 11840 16
6039.2.og \(\chi_{6039}(389, \cdot)\) n/a 11840 16
6039.2.oh \(\chi_{6039}(71, \cdot)\) n/a 3968 16
6039.2.ok \(\chi_{6039}(43, \cdot)\) n/a 11840 16
6039.2.oo \(\chi_{6039}(7, \cdot)\) n/a 11840 16
6039.2.op \(\chi_{6039}(139, \cdot)\) n/a 11840 16
6039.2.oq \(\chi_{6039}(337, \cdot)\) n/a 11840 16
6039.2.os \(\chi_{6039}(85, \cdot)\) n/a 11840 16
6039.2.ot \(\chi_{6039}(1063, \cdot)\) n/a 4928 16
6039.2.ow \(\chi_{6039}(542, \cdot)\) n/a 11840 16
6039.2.oz \(\chi_{6039}(59, \cdot)\) n/a 11840 16
6039.2.pb \(\chi_{6039}(871, \cdot)\) n/a 11840 16
6039.2.pc \(\chi_{6039}(238, \cdot)\) n/a 11840 16
6039.2.pd \(\chi_{6039}(40, \cdot)\) n/a 11840 16
6039.2.ph \(\chi_{6039}(340, \cdot)\) n/a 11840 16
6039.2.pi \(\chi_{6039}(254, \cdot)\) n/a 9920 16
6039.2.pm \(\chi_{6039}(284, \cdot)\) n/a 11840 16
6039.2.pn \(\chi_{6039}(185, \cdot)\) n/a 11840 16
6039.2.po \(\chi_{6039}(92, \cdot)\) n/a 11840 16
6039.2.pq \(\chi_{6039}(376, \cdot)\) n/a 11840 16
6039.2.ps \(\chi_{6039}(356, \cdot)\) n/a 11840 16
6039.2.pu \(\chi_{6039}(94, \cdot)\) n/a 11840 16
6039.2.pv \(\chi_{6039}(523, \cdot)\) n/a 4928 16
6039.2.qa \(\chi_{6039}(152, \cdot)\) n/a 3968 16
6039.2.qb \(\chi_{6039}(191, \cdot)\) n/a 11840 16
6039.2.qd \(\chi_{6039}(250, \cdot)\) n/a 11840 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6039))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6039)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(549))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(671))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2013))\)\(^{\oplus 2}\)