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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 the 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

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