# Properties

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

## 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

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