# Properties

 Label 2340.2 Level 2340 Weight 2 Dimension 60124 Nonzero newspaces 100 Sturm bound 580608 Trace bound 37

## Defining parameters

 Level: $$N$$ = $$2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$580608$$ Trace bound: $$37$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2340))$$.

Total New Old
Modular forms 148992 61308 87684
Cusp forms 141313 60124 81189
Eisenstein series 7679 1184 6495

## Trace form

 $$60124 q - 36 q^{2} - 48 q^{4} - 100 q^{5} - 124 q^{6} - 12 q^{7} - 36 q^{8} - 120 q^{9} + O(q^{10})$$ $$60124 q - 36 q^{2} - 48 q^{4} - 100 q^{5} - 124 q^{6} - 12 q^{7} - 36 q^{8} - 120 q^{9} - 150 q^{10} - 32 q^{11} - 8 q^{12} - 70 q^{13} - 6 q^{15} - 48 q^{16} - 50 q^{17} + 56 q^{18} - 32 q^{19} + 38 q^{20} - 236 q^{21} - 12 q^{22} + 24 q^{23} + 36 q^{24} - 92 q^{25} - 100 q^{26} + 48 q^{27} - 56 q^{28} - 30 q^{29} - 12 q^{30} - 72 q^{31} - 76 q^{32} - 12 q^{33} + 10 q^{35} - 180 q^{36} - 242 q^{37} - 20 q^{38} - 46 q^{39} - 226 q^{41} - 80 q^{42} - 92 q^{43} + 24 q^{44} + 18 q^{45} - 124 q^{46} - 12 q^{47} + 20 q^{48} - 146 q^{49} - 16 q^{50} + 48 q^{51} + 64 q^{52} - 32 q^{53} + 20 q^{54} - 26 q^{55} - 136 q^{56} + 104 q^{57} + 20 q^{58} + 16 q^{59} - 104 q^{60} - 138 q^{61} - 68 q^{62} + 92 q^{63} + 72 q^{64} - 68 q^{65} - 224 q^{66} + 48 q^{67} + 164 q^{68} - 20 q^{69} + 108 q^{70} + 96 q^{71} - 12 q^{72} - 40 q^{73} + 204 q^{74} - 18 q^{75} + 304 q^{76} + 228 q^{77} + 256 q^{78} + 108 q^{79} + 64 q^{80} - 288 q^{81} + 404 q^{82} + 228 q^{83} + 88 q^{84} + 183 q^{85} + 364 q^{86} - 68 q^{87} + 540 q^{88} + 20 q^{89} - 192 q^{90} + 148 q^{91} + 248 q^{92} + 52 q^{93} + 372 q^{94} - 96 q^{95} - 280 q^{96} + 68 q^{97} + 72 q^{98} - 44 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2340))$$

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
2340.2.a $$\chi_{2340}(1, \cdot)$$ 2340.2.a.a 1 1
2340.2.a.b 1
2340.2.a.c 1
2340.2.a.d 1
2340.2.a.e 1
2340.2.a.f 1
2340.2.a.g 1
2340.2.a.h 1
2340.2.a.i 1
2340.2.a.j 2
2340.2.a.k 2
2340.2.a.l 2
2340.2.a.m 2
2340.2.a.n 3
2340.2.c $$\chi_{2340}(181, \cdot)$$ 2340.2.c.a 2 1
2340.2.c.b 2
2340.2.c.c 4
2340.2.c.d 6
2340.2.c.e 8
2340.2.d $$\chi_{2340}(2339, \cdot)$$ n/a 168 1
2340.2.g $$\chi_{2340}(1691, \cdot)$$ 2340.2.g.a 48 1
2340.2.g.b 48
2340.2.h $$\chi_{2340}(469, \cdot)$$ 2340.2.h.a 2 1
2340.2.h.b 2
2340.2.h.c 4
2340.2.h.d 4
2340.2.h.e 6
2340.2.h.f 12
2340.2.j $$\chi_{2340}(649, \cdot)$$ 2340.2.j.a 4 1
2340.2.j.b 4
2340.2.j.c 8
2340.2.j.d 8
2340.2.j.e 12
2340.2.m $$\chi_{2340}(1871, \cdot)$$ n/a 112 1
2340.2.n $$\chi_{2340}(2159, \cdot)$$ n/a 144 1
2340.2.q $$\chi_{2340}(1621, \cdot)$$ 2340.2.q.a 2 2
2340.2.q.b 2
2340.2.q.c 2
2340.2.q.d 2
2340.2.q.e 2
2340.2.q.f 2
2340.2.q.g 4
2340.2.q.h 6
2340.2.q.i 6
2340.2.q.j 10
2340.2.q.k 10
2340.2.r $$\chi_{2340}(781, \cdot)$$ 2340.2.r.a 2 2
2340.2.r.b 2
2340.2.r.c 2
2340.2.r.d 14
2340.2.r.e 20
2340.2.r.f 26
2340.2.r.g 30
2340.2.s $$\chi_{2340}(601, \cdot)$$ n/a 112 2
2340.2.t $$\chi_{2340}(61, \cdot)$$ n/a 112 2
2340.2.u $$\chi_{2340}(73, \cdot)$$ 2340.2.u.a 2 2
2340.2.u.b 2
2340.2.u.c 2
2340.2.u.d 4
2340.2.u.e 4
2340.2.u.f 4
2340.2.u.g 8
2340.2.u.h 16
2340.2.u.i 28
2340.2.x $$\chi_{2340}(827, \cdot)$$ n/a 336 2
2340.2.y $$\chi_{2340}(53, \cdot)$$ 2340.2.y.a 24 2
2340.2.y.b 24
2340.2.bb $$\chi_{2340}(703, \cdot)$$ n/a 360 2
2340.2.bc $$\chi_{2340}(629, \cdot)$$ 2340.2.bc.a 56 2
2340.2.bf $$\chi_{2340}(811, \cdot)$$ n/a 280 2
2340.2.bh $$\chi_{2340}(1279, \cdot)$$ n/a 412 2
2340.2.bi $$\chi_{2340}(161, \cdot)$$ 2340.2.bi.a 4 2
2340.2.bi.b 4
2340.2.bi.c 12
2340.2.bi.d 12
2340.2.bk $$\chi_{2340}(883, \cdot)$$ n/a 412 2
2340.2.bn $$\chi_{2340}(233, \cdot)$$ 2340.2.bn.a 56 2
2340.2.bp $$\chi_{2340}(1477, \cdot)$$ 2340.2.bp.a 2 2
2340.2.bp.b 2
2340.2.bp.c 2
2340.2.bp.d 4
2340.2.bp.e 4
2340.2.bp.f 4
2340.2.bp.g 8
2340.2.bp.h 16
2340.2.bp.i 28
2340.2.bq $$\chi_{2340}(1763, \cdot)$$ n/a 336 2
2340.2.bs $$\chi_{2340}(529, \cdot)$$ n/a 168 2
2340.2.bv $$\chi_{2340}(191, \cdot)$$ n/a 672 2
2340.2.bw $$\chi_{2340}(959, \cdot)$$ n/a 992 2
2340.2.bz $$\chi_{2340}(1681, \cdot)$$ n/a 112 2
2340.2.ca $$\chi_{2340}(1031, \cdot)$$ n/a 672 2
2340.2.cd $$\chi_{2340}(589, \cdot)$$ n/a 168 2
2340.2.cg $$\chi_{2340}(1439, \cdot)$$ n/a 336 2
2340.2.ci $$\chi_{2340}(599, \cdot)$$ n/a 864 2
2340.2.cl $$\chi_{2340}(1429, \cdot)$$ n/a 168 2
2340.2.cm $$\chi_{2340}(311, \cdot)$$ n/a 672 2
2340.2.co $$\chi_{2340}(251, \cdot)$$ n/a 224 2
2340.2.cr $$\chi_{2340}(829, \cdot)$$ 2340.2.cr.a 16 2
2340.2.cr.b 24
2340.2.cr.c 32
2340.2.cu $$\chi_{2340}(1199, \cdot)$$ n/a 992 2
2340.2.cw $$\chi_{2340}(1499, \cdot)$$ n/a 992 2
2340.2.cx $$\chi_{2340}(121, \cdot)$$ n/a 112 2
2340.2.cz $$\chi_{2340}(131, \cdot)$$ n/a 576 2
2340.2.dc $$\chi_{2340}(1249, \cdot)$$ n/a 144 2
2340.2.de $$\chi_{2340}(289, \cdot)$$ 2340.2.de.a 12 2
2340.2.de.b 24
2340.2.de.c 32
2340.2.df $$\chi_{2340}(971, \cdot)$$ n/a 224 2
2340.2.di $$\chi_{2340}(179, \cdot)$$ n/a 336 2
2340.2.dj $$\chi_{2340}(361, \cdot)$$ 2340.2.dj.a 4 2
2340.2.dj.b 8
2340.2.dj.c 8
2340.2.dj.d 8
2340.2.dj.e 20
2340.2.dl $$\chi_{2340}(961, \cdot)$$ n/a 112 2
2340.2.do $$\chi_{2340}(779, \cdot)$$ n/a 992 2
2340.2.dq $$\chi_{2340}(1069, \cdot)$$ n/a 168 2
2340.2.dr $$\chi_{2340}(731, \cdot)$$ n/a 672 2
2340.2.du $$\chi_{2340}(419, \cdot)$$ n/a 992 2
2340.2.dx $$\chi_{2340}(491, \cdot)$$ n/a 672 2
2340.2.dy $$\chi_{2340}(49, \cdot)$$ n/a 168 2
2340.2.ea $$\chi_{2340}(167, \cdot)$$ n/a 1984 4
2340.2.ed $$\chi_{2340}(97, \cdot)$$ n/a 336 4
2340.2.ee $$\chi_{2340}(817, \cdot)$$ n/a 336 4
2340.2.eg $$\chi_{2340}(203, \cdot)$$ n/a 1984 4
2340.2.ei $$\chi_{2340}(323, \cdot)$$ n/a 672 4
2340.2.el $$\chi_{2340}(37, \cdot)$$ n/a 140 4
2340.2.en $$\chi_{2340}(697, \cdot)$$ n/a 336 4
2340.2.ep $$\chi_{2340}(587, \cdot)$$ n/a 1984 4
2340.2.eq $$\chi_{2340}(367, \cdot)$$ n/a 1984 4
2340.2.et $$\chi_{2340}(113, \cdot)$$ n/a 336 4
2340.2.ev $$\chi_{2340}(103, \cdot)$$ n/a 1984 4
2340.2.ew $$\chi_{2340}(17, \cdot)$$ n/a 112 4
2340.2.ez $$\chi_{2340}(173, \cdot)$$ n/a 336 4
2340.2.fa $$\chi_{2340}(43, \cdot)$$ n/a 1984 4
2340.2.fd $$\chi_{2340}(127, \cdot)$$ n/a 824 4
2340.2.fe $$\chi_{2340}(77, \cdot)$$ n/a 336 4
2340.2.fg $$\chi_{2340}(31, \cdot)$$ n/a 1344 4
2340.2.fj $$\chi_{2340}(749, \cdot)$$ n/a 336 4
2340.2.fk $$\chi_{2340}(799, \cdot)$$ n/a 1984 4
2340.2.fm $$\chi_{2340}(761, \cdot)$$ n/a 224 4
2340.2.fo $$\chi_{2340}(1241, \cdot)$$ 2340.2.fo.a 40 4
2340.2.fo.b 40
2340.2.fr $$\chi_{2340}(19, \cdot)$$ n/a 824 4
2340.2.ft $$\chi_{2340}(319, \cdot)$$ n/a 1984 4
2340.2.fv $$\chi_{2340}(41, \cdot)$$ n/a 224 4
2340.2.fx $$\chi_{2340}(509, \cdot)$$ n/a 336 4
2340.2.fz $$\chi_{2340}(271, \cdot)$$ n/a 560 4
2340.2.gb $$\chi_{2340}(691, \cdot)$$ n/a 1344 4
2340.2.gc $$\chi_{2340}(149, \cdot)$$ n/a 336 4
2340.2.ge $$\chi_{2340}(89, \cdot)$$ n/a 112 4
2340.2.gg $$\chi_{2340}(331, \cdot)$$ n/a 1344 4
2340.2.gj $$\chi_{2340}(281, \cdot)$$ n/a 224 4
2340.2.gk $$\chi_{2340}(499, \cdot)$$ n/a 1984 4
2340.2.gn $$\chi_{2340}(677, \cdot)$$ n/a 288 4
2340.2.go $$\chi_{2340}(523, \cdot)$$ n/a 824 4
2340.2.gr $$\chi_{2340}(763, \cdot)$$ n/a 1984 4
2340.2.gs $$\chi_{2340}(653, \cdot)$$ n/a 336 4
2340.2.gv $$\chi_{2340}(737, \cdot)$$ n/a 112 4
2340.2.gw $$\chi_{2340}(547, \cdot)$$ n/a 1728 4
2340.2.gy $$\chi_{2340}(797, \cdot)$$ n/a 336 4
2340.2.hb $$\chi_{2340}(823, \cdot)$$ n/a 1984 4
2340.2.hd $$\chi_{2340}(457, \cdot)$$ n/a 336 4
2340.2.hf $$\chi_{2340}(1727, \cdot)$$ n/a 672 4
2340.2.hh $$\chi_{2340}(47, \cdot)$$ n/a 1984 4
2340.2.hi $$\chi_{2340}(853, \cdot)$$ n/a 336 4
2340.2.hk $$\chi_{2340}(973, \cdot)$$ n/a 140 4
2340.2.hm $$\chi_{2340}(383, \cdot)$$ n/a 1984 4
2340.2.hp $$\chi_{2340}(227, \cdot)$$ n/a 1984 4
2340.2.hq $$\chi_{2340}(1033, \cdot)$$ n/a 336 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2340))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2340)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(234))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(468))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(780))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1170))$$$$^{\oplus 2}$$