↑

Properties

Label 1680.3
Level 1680
Weight 3
Dimension 54376
Nonzero newspaces 56
Sturm bound 442368
Trace bound 25

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(442368\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1680))\).

Total New Old
Modular forms 150144 54920 95224
Cusp forms 144768 54376 90392
Eisenstein series 5376 544 4832

Trace form

\( 54376 q - 10 q^{3} + 16 q^{4} + 24 q^{5} - 24 q^{6} - 4 q^{7} - 48 q^{8} - 42 q^{9} + O(q^{10}) \) \( 54376 q - 10 q^{3} + 16 q^{4} + 24 q^{5} - 24 q^{6} - 4 q^{7} - 48 q^{8} - 42 q^{9} - 200 q^{10} + 128 q^{11} - 232 q^{12} - 48 q^{13} - 88 q^{14} - 18 q^{15} - 16 q^{16} + 16 q^{17} - 200 q^{18} - 220 q^{19} + 160 q^{20} - 10 q^{21} + 224 q^{22} - 416 q^{23} - 88 q^{24} + 10 q^{25} - 400 q^{26} - 112 q^{27} - 288 q^{28} - 208 q^{29} - 284 q^{30} - 372 q^{31} - 480 q^{32} - 326 q^{33} - 368 q^{34} - 288 q^{35} + 624 q^{36} - 956 q^{37} + 448 q^{38} - 568 q^{39} + 552 q^{40} - 176 q^{41} - 200 q^{42} - 280 q^{43} - 640 q^{44} - 461 q^{45} - 704 q^{46} - 192 q^{47} - 664 q^{48} + 512 q^{49} + 848 q^{50} + 50 q^{51} - 1120 q^{52} - 720 q^{53} - 1000 q^{54} - 244 q^{55} - 112 q^{56} + 84 q^{57} - 704 q^{58} - 128 q^{59} - 220 q^{60} - 172 q^{61} + 1920 q^{62} + 302 q^{63} + 1840 q^{64} + 336 q^{65} + 2264 q^{66} - 756 q^{67} + 3792 q^{68} + 708 q^{69} + 2608 q^{70} - 128 q^{71} + 2200 q^{72} + 1220 q^{73} + 3152 q^{74} - 315 q^{75} + 4080 q^{76} + 928 q^{77} + 2864 q^{78} + 1492 q^{79} + 784 q^{80} - 278 q^{81} + 1936 q^{82} + 1728 q^{83} + 1128 q^{84} + 2116 q^{85} + 320 q^{86} + 2948 q^{87} + 144 q^{88} + 1392 q^{89} - 692 q^{90} - 392 q^{91} - 848 q^{92} + 1426 q^{93} + 1424 q^{94} + 1344 q^{95} + 1416 q^{96} + 16 q^{97} + 2576 q^{98} + 588 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1680))\)

We only show spaces with odd 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
1680.3.b \(\chi_{1680}(839, \cdot)\) None 0 1
1680.3.c \(\chi_{1680}(799, \cdot)\) 1680.3.c.a 24 1
1680.3.c.b 48
1680.3.h \(\chi_{1680}(1609, \cdot)\) None 0 1
1680.3.i \(\chi_{1680}(449, \cdot)\) n/a 144 1
1680.3.l \(\chi_{1680}(1121, \cdot)\) 1680.3.l.a 16 1
1680.3.l.b 16
1680.3.l.c 16
1680.3.l.d 48
1680.3.m \(\chi_{1680}(601, \cdot)\) None 0 1
1680.3.n \(\chi_{1680}(1471, \cdot)\) 1680.3.n.a 16 1
1680.3.n.b 16
1680.3.n.c 16
1680.3.o \(\chi_{1680}(1511, \cdot)\) None 0 1
1680.3.r \(\chi_{1680}(281, \cdot)\) None 0 1
1680.3.s \(\chi_{1680}(1441, \cdot)\) 1680.3.s.a 8 1
1680.3.s.b 12
1680.3.s.c 12
1680.3.s.d 32
1680.3.x \(\chi_{1680}(631, \cdot)\) None 0 1
1680.3.y \(\chi_{1680}(671, \cdot)\) n/a 128 1
1680.3.bb \(\chi_{1680}(1679, \cdot)\) n/a 192 1
1680.3.bc \(\chi_{1680}(1639, \cdot)\) None 0 1
1680.3.bd \(\chi_{1680}(769, \cdot)\) 1680.3.bd.a 16 1
1680.3.bd.b 16
1680.3.bd.c 16
1680.3.bd.d 48
1680.3.be \(\chi_{1680}(1289, \cdot)\) None 0 1
1680.3.bh \(\chi_{1680}(407, \cdot)\) None 0 2
1680.3.bi \(\chi_{1680}(223, \cdot)\) n/a 192 2
1680.3.bn \(\chi_{1680}(1217, \cdot)\) n/a 376 2
1680.3.bo \(\chi_{1680}(1177, \cdot)\) None 0 2
1680.3.bq \(\chi_{1680}(323, \cdot)\) n/a 1152 2
1680.3.br \(\chi_{1680}(293, \cdot)\) n/a 1520 2
1680.3.bt \(\chi_{1680}(253, \cdot)\) n/a 576 2
1680.3.bw \(\chi_{1680}(307, \cdot)\) n/a 768 2
1680.3.by \(\chi_{1680}(379, \cdot)\) n/a 576 2
1680.3.bz \(\chi_{1680}(181, \cdot)\) n/a 512 2
1680.3.cc \(\chi_{1680}(419, \cdot)\) n/a 1520 2
1680.3.cd \(\chi_{1680}(701, \cdot)\) n/a 768 2
1680.3.cf \(\chi_{1680}(251, \cdot)\) n/a 1024 2
1680.3.ci \(\chi_{1680}(29, \cdot)\) n/a 1152 2
1680.3.cj \(\chi_{1680}(211, \cdot)\) n/a 384 2
1680.3.cm \(\chi_{1680}(349, \cdot)\) n/a 768 2
1680.3.cn \(\chi_{1680}(1133, \cdot)\) n/a 1520 2
1680.3.cq \(\chi_{1680}(1163, \cdot)\) n/a 1152 2
1680.3.cs \(\chi_{1680}(643, \cdot)\) n/a 768 2
1680.3.ct \(\chi_{1680}(1093, \cdot)\) n/a 576 2
1680.3.cv \(\chi_{1680}(377, \cdot)\) None 0 2
1680.3.cw \(\chi_{1680}(337, \cdot)\) n/a 144 2
1680.3.db \(\chi_{1680}(1247, \cdot)\) n/a 288 2
1680.3.dc \(\chi_{1680}(727, \cdot)\) None 0 2
1680.3.dd \(\chi_{1680}(1151, \cdot)\) n/a 256 2
1680.3.de \(\chi_{1680}(151, \cdot)\) None 0 2
1680.3.dj \(\chi_{1680}(241, \cdot)\) n/a 128 2
1680.3.dk \(\chi_{1680}(1241, \cdot)\) None 0 2
1680.3.dm \(\chi_{1680}(569, \cdot)\) None 0 2
1680.3.dn \(\chi_{1680}(1249, \cdot)\) n/a 192 2
1680.3.do \(\chi_{1680}(919, \cdot)\) None 0 2
1680.3.dp \(\chi_{1680}(479, \cdot)\) n/a 384 2
1680.3.ds \(\chi_{1680}(1409, \cdot)\) n/a 376 2
1680.3.dt \(\chi_{1680}(409, \cdot)\) None 0 2
1680.3.dy \(\chi_{1680}(79, \cdot)\) n/a 192 2
1680.3.dz \(\chi_{1680}(1319, \cdot)\) None 0 2
1680.3.ec \(\chi_{1680}(311, \cdot)\) None 0 2
1680.3.ed \(\chi_{1680}(751, \cdot)\) n/a 128 2
1680.3.ee \(\chi_{1680}(1081, \cdot)\) None 0 2
1680.3.ef \(\chi_{1680}(401, \cdot)\) n/a 256 2
1680.3.ek \(\chi_{1680}(103, \cdot)\) None 0 4
1680.3.el \(\chi_{1680}(527, \cdot)\) n/a 768 4
1680.3.em \(\chi_{1680}(193, \cdot)\) n/a 384 4
1680.3.en \(\chi_{1680}(857, \cdot)\) None 0 4
1680.3.er \(\chi_{1680}(283, \cdot)\) n/a 1536 4
1680.3.es \(\chi_{1680}(37, \cdot)\) n/a 1536 4
1680.3.eu \(\chi_{1680}(773, \cdot)\) n/a 3040 4
1680.3.ex \(\chi_{1680}(107, \cdot)\) n/a 3040 4
1680.3.ez \(\chi_{1680}(331, \cdot)\) n/a 1024 4
1680.3.fa \(\chi_{1680}(229, \cdot)\) n/a 1536 4
1680.3.fd \(\chi_{1680}(131, \cdot)\) n/a 2048 4
1680.3.fe \(\chi_{1680}(149, \cdot)\) n/a 3040 4
1680.3.fg \(\chi_{1680}(59, \cdot)\) n/a 3040 4
1680.3.fj \(\chi_{1680}(221, \cdot)\) n/a 2048 4
1680.3.fk \(\chi_{1680}(499, \cdot)\) n/a 1536 4
1680.3.fn \(\chi_{1680}(61, \cdot)\) n/a 1024 4
1680.3.fo \(\chi_{1680}(373, \cdot)\) n/a 1536 4
1680.3.fr \(\chi_{1680}(187, \cdot)\) n/a 1536 4
1680.3.ft \(\chi_{1680}(443, \cdot)\) n/a 3040 4
1680.3.fu \(\chi_{1680}(173, \cdot)\) n/a 3040 4
1680.3.fy \(\chi_{1680}(457, \cdot)\) None 0 4
1680.3.fz \(\chi_{1680}(17, \cdot)\) n/a 752 4
1680.3.ga \(\chi_{1680}(367, \cdot)\) n/a 384 4
1680.3.gb \(\chi_{1680}(23, \cdot)\) None 0 4

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1680))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1680)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 2}\)