# Properties

 Label 3120.2 Level 3120 Weight 2 Dimension 98012 Nonzero newspaces 104 Sturm bound 1032192 Trace bound 49

## Defining parameters

 Level: $$N$$ = $$3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$104$$ Sturm bound: $$1032192$$ Trace bound: $$49$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3120))$$.

Total New Old
Modular forms 263424 99196 164228
Cusp forms 252673 98012 154661
Eisenstein series 10751 1184 9567

## Trace form

 $$98012 q - 28 q^{3} - 96 q^{4} - 4 q^{5} - 144 q^{6} - 80 q^{7} - 48 q^{8} - 32 q^{9} + O(q^{10})$$ $$98012 q - 28 q^{3} - 96 q^{4} - 4 q^{5} - 144 q^{6} - 80 q^{7} - 48 q^{8} - 32 q^{9} - 128 q^{10} - 48 q^{11} - 32 q^{12} - 128 q^{13} + 48 q^{14} - 86 q^{15} - 160 q^{16} - 24 q^{17} - 152 q^{19} + 32 q^{20} - 156 q^{21} - 16 q^{23} + 80 q^{24} - 44 q^{25} + 40 q^{26} - 40 q^{27} + 64 q^{28} - 24 q^{29} + 48 q^{30} - 72 q^{31} + 160 q^{32} - 52 q^{33} + 160 q^{34} + 96 q^{35} - 16 q^{36} - 56 q^{37} + 192 q^{38} + 8 q^{39} + 16 q^{40} + 8 q^{41} - 48 q^{42} - 176 q^{43} + 64 q^{44} - 70 q^{45} - 160 q^{46} - 96 q^{47} - 160 q^{48} - 396 q^{49} + 128 q^{50} - 16 q^{51} - 80 q^{52} - 104 q^{53} - 224 q^{54} - 124 q^{55} - 84 q^{57} - 32 q^{59} - 104 q^{60} - 304 q^{61} - 48 q^{62} + 196 q^{63} + 96 q^{64} - 52 q^{65} - 176 q^{66} + 208 q^{67} - 96 q^{68} + 164 q^{69} - 256 q^{70} + 288 q^{71} - 128 q^{72} + 88 q^{73} - 144 q^{74} + 252 q^{75} - 224 q^{76} + 160 q^{77} - 112 q^{78} + 192 q^{79} - 304 q^{80} - 192 q^{81} - 224 q^{82} + 208 q^{83} - 32 q^{84} - 52 q^{85} + 64 q^{86} + 52 q^{87} - 64 q^{88} + 280 q^{89} - 32 q^{90} - 64 q^{91} + 224 q^{92} + 276 q^{93} + 320 q^{94} + 152 q^{95} + 400 q^{96} - 8 q^{97} + 608 q^{98} + 60 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3120))$$

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
3120.2.a $$\chi_{3120}(1, \cdot)$$ 3120.2.a.a 1 1
3120.2.a.b 1
3120.2.a.c 1
3120.2.a.d 1
3120.2.a.e 1
3120.2.a.f 1
3120.2.a.g 1
3120.2.a.h 1
3120.2.a.i 1
3120.2.a.j 1
3120.2.a.k 1
3120.2.a.l 1
3120.2.a.m 1
3120.2.a.n 1
3120.2.a.o 1
3120.2.a.p 1
3120.2.a.q 1
3120.2.a.r 1
3120.2.a.s 1
3120.2.a.t 1
3120.2.a.u 1
3120.2.a.v 1
3120.2.a.w 1
3120.2.a.x 1
3120.2.a.y 1
3120.2.a.z 1
3120.2.a.ba 1
3120.2.a.bb 2
3120.2.a.bc 2
3120.2.a.bd 2
3120.2.a.be 2
3120.2.a.bf 2
3120.2.a.bg 2
3120.2.a.bh 3
3120.2.a.bi 3
3120.2.a.bj 3
3120.2.b $$\chi_{3120}(2809, \cdot)$$ None 0 1
3120.2.e $$\chi_{3120}(2471, \cdot)$$ None 0 1
3120.2.g $$\chi_{3120}(961, \cdot)$$ 3120.2.g.a 2 1
3120.2.g.b 2
3120.2.g.c 2
3120.2.g.d 2
3120.2.g.e 2
3120.2.g.f 2
3120.2.g.g 2
3120.2.g.h 2
3120.2.g.i 2
3120.2.g.j 2
3120.2.g.k 2
3120.2.g.l 4
3120.2.g.m 4
3120.2.g.n 4
3120.2.g.o 4
3120.2.g.p 4
3120.2.g.q 4
3120.2.g.r 4
3120.2.g.s 6
3120.2.h $$\chi_{3120}(3119, \cdot)$$ n/a 168 1
3120.2.k $$\chi_{3120}(911, \cdot)$$ 3120.2.k.a 4 1
3120.2.k.b 4
3120.2.k.c 4
3120.2.k.d 4
3120.2.k.e 4
3120.2.k.f 8
3120.2.k.g 16
3120.2.k.h 20
3120.2.k.i 32
3120.2.l $$\chi_{3120}(1249, \cdot)$$ 3120.2.l.a 2 1
3120.2.l.b 2
3120.2.l.c 2
3120.2.l.d 2
3120.2.l.e 2
3120.2.l.f 2
3120.2.l.g 2
3120.2.l.h 2
3120.2.l.i 2
3120.2.l.j 4
3120.2.l.k 4
3120.2.l.l 4
3120.2.l.m 6
3120.2.l.n 8
3120.2.l.o 8
3120.2.l.p 10
3120.2.l.q 10
3120.2.n $$\chi_{3120}(1559, \cdot)$$ None 0 1
3120.2.q $$\chi_{3120}(2521, \cdot)$$ None 0 1
3120.2.r $$\chi_{3120}(2209, \cdot)$$ 3120.2.r.a 2 1
3120.2.r.b 2
3120.2.r.c 2
3120.2.r.d 2
3120.2.r.e 2
3120.2.r.f 2
3120.2.r.g 6
3120.2.r.h 6
3120.2.r.i 8
3120.2.r.j 8
3120.2.r.k 10
3120.2.r.l 10
3120.2.r.m 12
3120.2.r.n 12
3120.2.u $$\chi_{3120}(1871, \cdot)$$ n/a 112 1
3120.2.w $$\chi_{3120}(1561, \cdot)$$ None 0 1
3120.2.x $$\chi_{3120}(599, \cdot)$$ None 0 1
3120.2.ba $$\chi_{3120}(311, \cdot)$$ None 0 1
3120.2.bb $$\chi_{3120}(649, \cdot)$$ None 0 1
3120.2.bd $$\chi_{3120}(2159, \cdot)$$ n/a 144 1
3120.2.bg $$\chi_{3120}(2161, \cdot)$$ n/a 112 2
3120.2.bi $$\chi_{3120}(1763, \cdot)$$ n/a 1328 2
3120.2.bk $$\chi_{3120}(2293, \cdot)$$ n/a 672 2
3120.2.bm $$\chi_{3120}(1091, \cdot)$$ n/a 896 2
3120.2.bn $$\chi_{3120}(1429, \cdot)$$ n/a 672 2
3120.2.bp $$\chi_{3120}(577, \cdot)$$ n/a 168 2
3120.2.bq $$\chi_{3120}(1607, \cdot)$$ None 0 2
3120.2.bv $$\chi_{3120}(73, \cdot)$$ None 0 2
3120.2.bw $$\chi_{3120}(47, \cdot)$$ n/a 336 2
3120.2.by $$\chi_{3120}(781, \cdot)$$ n/a 384 2
3120.2.bz $$\chi_{3120}(1379, \cdot)$$ n/a 1152 2
3120.2.cb $$\chi_{3120}(733, \cdot)$$ n/a 672 2
3120.2.cd $$\chi_{3120}(203, \cdot)$$ n/a 1328 2
3120.2.cf $$\chi_{3120}(2371, \cdot)$$ n/a 448 2
3120.2.ci $$\chi_{3120}(2189, \cdot)$$ n/a 1328 2
3120.2.ck $$\chi_{3120}(233, \cdot)$$ None 0 2
3120.2.cl $$\chi_{3120}(833, \cdot)$$ n/a 288 2
3120.2.co $$\chi_{3120}(703, \cdot)$$ n/a 144 2
3120.2.cp $$\chi_{3120}(103, \cdot)$$ None 0 2
3120.2.cs $$\chi_{3120}(499, \cdot)$$ n/a 672 2
3120.2.ct $$\chi_{3120}(941, \cdot)$$ n/a 896 2
3120.2.cw $$\chi_{3120}(1409, \cdot)$$ n/a 328 2
3120.2.cx $$\chi_{3120}(1529, \cdot)$$ None 0 2
3120.2.cz $$\chi_{3120}(151, \cdot)$$ None 0 2
3120.2.dc $$\chi_{3120}(31, \cdot)$$ n/a 112 2
3120.2.dd $$\chi_{3120}(2107, \cdot)$$ n/a 576 2
3120.2.de $$\chi_{3120}(77, \cdot)$$ n/a 1328 2
3120.2.dh $$\chi_{3120}(1637, \cdot)$$ n/a 1328 2
3120.2.di $$\chi_{3120}(547, \cdot)$$ n/a 576 2
3120.2.dn $$\chi_{3120}(1507, \cdot)$$ n/a 672 2
3120.2.do $$\chi_{3120}(677, \cdot)$$ n/a 1152 2
3120.2.dr $$\chi_{3120}(53, \cdot)$$ n/a 1152 2
3120.2.ds $$\chi_{3120}(883, \cdot)$$ n/a 672 2
3120.2.du $$\chi_{3120}(1399, \cdot)$$ None 0 2
3120.2.dv $$\chi_{3120}(1279, \cdot)$$ n/a 168 2
3120.2.dx $$\chi_{3120}(161, \cdot)$$ n/a 224 2
3120.2.ea $$\chi_{3120}(281, \cdot)$$ None 0 2
3120.2.ec $$\chi_{3120}(629, \cdot)$$ n/a 1328 2
3120.2.ed $$\chi_{3120}(811, \cdot)$$ n/a 448 2
3120.2.ef $$\chi_{3120}(1663, \cdot)$$ n/a 168 2
3120.2.ei $$\chi_{3120}(2263, \cdot)$$ None 0 2
3120.2.ej $$\chi_{3120}(2393, \cdot)$$ None 0 2
3120.2.em $$\chi_{3120}(1793, \cdot)$$ n/a 328 2
3120.2.en $$\chi_{3120}(2501, \cdot)$$ n/a 896 2
3120.2.eq $$\chi_{3120}(2059, \cdot)$$ n/a 672 2
3120.2.er $$\chi_{3120}(1643, \cdot)$$ n/a 1328 2
3120.2.et $$\chi_{3120}(2413, \cdot)$$ n/a 672 2
3120.2.ev $$\chi_{3120}(131, \cdot)$$ n/a 768 2
3120.2.ey $$\chi_{3120}(469, \cdot)$$ n/a 576 2
3120.2.fb $$\chi_{3120}(983, \cdot)$$ None 0 2
3120.2.fc $$\chi_{3120}(2257, \cdot)$$ n/a 168 2
3120.2.fd $$\chi_{3120}(1487, \cdot)$$ n/a 336 2
3120.2.fe $$\chi_{3120}(697, \cdot)$$ None 0 2
3120.2.fh $$\chi_{3120}(181, \cdot)$$ n/a 448 2
3120.2.fk $$\chi_{3120}(779, \cdot)$$ n/a 1328 2
3120.2.fm $$\chi_{3120}(853, \cdot)$$ n/a 672 2
3120.2.fo $$\chi_{3120}(83, \cdot)$$ n/a 1328 2
3120.2.fr $$\chi_{3120}(1199, \cdot)$$ n/a 336 2
3120.2.ft $$\chi_{3120}(1369, \cdot)$$ None 0 2
3120.2.fu $$\chi_{3120}(1031, \cdot)$$ None 0 2
3120.2.fx $$\chi_{3120}(2759, \cdot)$$ None 0 2
3120.2.fy $$\chi_{3120}(601, \cdot)$$ None 0 2
3120.2.ga $$\chi_{3120}(2591, \cdot)$$ n/a 224 2
3120.2.gd $$\chi_{3120}(49, \cdot)$$ n/a 168 2
3120.2.ge $$\chi_{3120}(121, \cdot)$$ None 0 2
3120.2.gh $$\chi_{3120}(2279, \cdot)$$ None 0 2
3120.2.gj $$\chi_{3120}(289, \cdot)$$ n/a 168 2
3120.2.gk $$\chi_{3120}(191, \cdot)$$ n/a 224 2
3120.2.gn $$\chi_{3120}(719, \cdot)$$ n/a 336 2
3120.2.go $$\chi_{3120}(1681, \cdot)$$ n/a 112 2
3120.2.gq $$\chi_{3120}(1511, \cdot)$$ None 0 2
3120.2.gt $$\chi_{3120}(1849, \cdot)$$ None 0 2
3120.2.gu $$\chi_{3120}(1307, \cdot)$$ n/a 2656 4
3120.2.gw $$\chi_{3120}(877, \cdot)$$ n/a 1344 4
3120.2.gz $$\chi_{3120}(179, \cdot)$$ n/a 2656 4
3120.2.ha $$\chi_{3120}(901, \cdot)$$ n/a 896 4
3120.2.he $$\chi_{3120}(1007, \cdot)$$ n/a 672 4
3120.2.hf $$\chi_{3120}(1033, \cdot)$$ None 0 4
3120.2.hg $$\chi_{3120}(1367, \cdot)$$ None 0 4
3120.2.hh $$\chi_{3120}(817, \cdot)$$ n/a 336 4
3120.2.hl $$\chi_{3120}(1069, \cdot)$$ n/a 1344 4
3120.2.hm $$\chi_{3120}(731, \cdot)$$ n/a 1792 4
3120.2.hp $$\chi_{3120}(973, \cdot)$$ n/a 1344 4
3120.2.hr $$\chi_{3120}(947, \cdot)$$ n/a 2656 4
3120.2.hs $$\chi_{3120}(379, \cdot)$$ n/a 1344 4
3120.2.hv $$\chi_{3120}(821, \cdot)$$ n/a 1792 4
3120.2.hw $$\chi_{3120}(17, \cdot)$$ n/a 656 4
3120.2.hz $$\chi_{3120}(1433, \cdot)$$ None 0 4
3120.2.ia $$\chi_{3120}(1303, \cdot)$$ None 0 4
3120.2.id $$\chi_{3120}(127, \cdot)$$ n/a 336 4
3120.2.if $$\chi_{3120}(331, \cdot)$$ n/a 896 4
3120.2.ig $$\chi_{3120}(149, \cdot)$$ n/a 2656 4
3120.2.ij $$\chi_{3120}(41, \cdot)$$ None 0 4
3120.2.ik $$\chi_{3120}(401, \cdot)$$ n/a 448 4
3120.2.im $$\chi_{3120}(319, \cdot)$$ n/a 336 4
3120.2.ip $$\chi_{3120}(1159, \cdot)$$ None 0 4
3120.2.is $$\chi_{3120}(523, \cdot)$$ n/a 1344 4
3120.2.it $$\chi_{3120}(173, \cdot)$$ n/a 2656 4
3120.2.iw $$\chi_{3120}(797, \cdot)$$ n/a 2656 4
3120.2.ix $$\chi_{3120}(1147, \cdot)$$ n/a 1344 4
3120.2.iy $$\chi_{3120}(667, \cdot)$$ n/a 1344 4
3120.2.iz $$\chi_{3120}(1277, \cdot)$$ n/a 2656 4
3120.2.jc $$\chi_{3120}(653, \cdot)$$ n/a 2656 4
3120.2.jd $$\chi_{3120}(43, \cdot)$$ n/a 1344 4
3120.2.jh $$\chi_{3120}(271, \cdot)$$ n/a 224 4
3120.2.ji $$\chi_{3120}(631, \cdot)$$ None 0 4
3120.2.jk $$\chi_{3120}(89, \cdot)$$ None 0 4
3120.2.jn $$\chi_{3120}(449, \cdot)$$ n/a 656 4
3120.2.jp $$\chi_{3120}(461, \cdot)$$ n/a 1792 4
3120.2.jq $$\chi_{3120}(19, \cdot)$$ n/a 1344 4
3120.2.jt $$\chi_{3120}(823, \cdot)$$ None 0 4
3120.2.ju $$\chi_{3120}(367, \cdot)$$ n/a 336 4
3120.2.jx $$\chi_{3120}(113, \cdot)$$ n/a 656 4
3120.2.jy $$\chi_{3120}(953, \cdot)$$ None 0 4
3120.2.ka $$\chi_{3120}(509, \cdot)$$ n/a 2656 4
3120.2.kd $$\chi_{3120}(691, \cdot)$$ n/a 896 4
3120.2.kf $$\chi_{3120}(227, \cdot)$$ n/a 2656 4
3120.2.kh $$\chi_{3120}(37, \cdot)$$ n/a 1344 4
3120.2.ki $$\chi_{3120}(419, \cdot)$$ n/a 2656 4
3120.2.kl $$\chi_{3120}(61, \cdot)$$ n/a 896 4
3120.2.km $$\chi_{3120}(457, \cdot)$$ None 0 4
3120.2.kn $$\chi_{3120}(383, \cdot)$$ n/a 672 4
3120.2.ks $$\chi_{3120}(97, \cdot)$$ n/a 336 4
3120.2.kt $$\chi_{3120}(167, \cdot)$$ None 0 4
3120.2.ku $$\chi_{3120}(589, \cdot)$$ n/a 1344 4
3120.2.kx $$\chi_{3120}(251, \cdot)$$ n/a 1792 4
3120.2.ky $$\chi_{3120}(397, \cdot)$$ n/a 1344 4
3120.2.la $$\chi_{3120}(323, \cdot)$$ n/a 2656 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3120))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3120)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(780))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1040))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1560))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3120))$$$$^{\oplus 1}$$