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Properties

Label 1680.1
Level 1680
Weight 1
Dimension 24
Nonzero newspaces 2
Newform subspaces 12
Sturm bound 147456
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 12 \)
Sturm bound: \(147456\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1680))\).

Total New Old
Modular forms 3004 296 2708
Cusp forms 316 24 292
Eisenstein series 2688 272 2416

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q + 6 q^{9} + O(q^{10}) \) \( 24 q + 6 q^{9} + 6 q^{21} - 12 q^{25} - 6 q^{45} - 12 q^{49} + 12 q^{61} + 6 q^{81} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1680))\)

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
1680.1.b \(\chi_{1680}(839, \cdot)\) None 0 1
1680.1.c \(\chi_{1680}(799, \cdot)\) None 0 1
1680.1.h \(\chi_{1680}(1609, \cdot)\) None 0 1
1680.1.i \(\chi_{1680}(449, \cdot)\) None 0 1
1680.1.l \(\chi_{1680}(1121, \cdot)\) None 0 1
1680.1.m \(\chi_{1680}(601, \cdot)\) None 0 1
1680.1.n \(\chi_{1680}(1471, \cdot)\) None 0 1
1680.1.o \(\chi_{1680}(1511, \cdot)\) None 0 1
1680.1.r \(\chi_{1680}(281, \cdot)\) None 0 1
1680.1.s \(\chi_{1680}(1441, \cdot)\) None 0 1
1680.1.x \(\chi_{1680}(631, \cdot)\) None 0 1
1680.1.y \(\chi_{1680}(671, \cdot)\) None 0 1
1680.1.bb \(\chi_{1680}(1679, \cdot)\) 1680.1.bb.a 1 1
1680.1.bb.b 1
1680.1.bb.c 1
1680.1.bb.d 1
1680.1.bb.e 2
1680.1.bb.f 2
1680.1.bb.g 4
1680.1.bb.h 4
1680.1.bc \(\chi_{1680}(1639, \cdot)\) None 0 1
1680.1.bd \(\chi_{1680}(769, \cdot)\) None 0 1
1680.1.be \(\chi_{1680}(1289, \cdot)\) None 0 1
1680.1.bh \(\chi_{1680}(407, \cdot)\) None 0 2
1680.1.bi \(\chi_{1680}(223, \cdot)\) None 0 2
1680.1.bn \(\chi_{1680}(1217, \cdot)\) None 0 2
1680.1.bo \(\chi_{1680}(1177, \cdot)\) None 0 2
1680.1.bq \(\chi_{1680}(323, \cdot)\) None 0 2
1680.1.br \(\chi_{1680}(293, \cdot)\) None 0 2
1680.1.bt \(\chi_{1680}(253, \cdot)\) None 0 2
1680.1.bw \(\chi_{1680}(307, \cdot)\) None 0 2
1680.1.by \(\chi_{1680}(379, \cdot)\) None 0 2
1680.1.bz \(\chi_{1680}(181, \cdot)\) None 0 2
1680.1.cc \(\chi_{1680}(419, \cdot)\) None 0 2
1680.1.cd \(\chi_{1680}(701, \cdot)\) None 0 2
1680.1.cf \(\chi_{1680}(251, \cdot)\) None 0 2
1680.1.ci \(\chi_{1680}(29, \cdot)\) None 0 2
1680.1.cj \(\chi_{1680}(211, \cdot)\) None 0 2
1680.1.cm \(\chi_{1680}(349, \cdot)\) None 0 2
1680.1.cn \(\chi_{1680}(1133, \cdot)\) None 0 2
1680.1.cq \(\chi_{1680}(1163, \cdot)\) None 0 2
1680.1.cs \(\chi_{1680}(643, \cdot)\) None 0 2
1680.1.ct \(\chi_{1680}(1093, \cdot)\) None 0 2
1680.1.cv \(\chi_{1680}(377, \cdot)\) None 0 2
1680.1.cw \(\chi_{1680}(337, \cdot)\) None 0 2
1680.1.db \(\chi_{1680}(1247, \cdot)\) None 0 2
1680.1.dc \(\chi_{1680}(727, \cdot)\) None 0 2
1680.1.dd \(\chi_{1680}(1151, \cdot)\) None 0 2
1680.1.de \(\chi_{1680}(151, \cdot)\) None 0 2
1680.1.dj \(\chi_{1680}(241, \cdot)\) None 0 2
1680.1.dk \(\chi_{1680}(1241, \cdot)\) None 0 2
1680.1.dm \(\chi_{1680}(569, \cdot)\) None 0 2
1680.1.dn \(\chi_{1680}(1249, \cdot)\) None 0 2
1680.1.do \(\chi_{1680}(919, \cdot)\) None 0 2
1680.1.dp \(\chi_{1680}(479, \cdot)\) 1680.1.dp.a 2 2
1680.1.dp.b 2
1680.1.dp.c 2
1680.1.dp.d 2
1680.1.ds \(\chi_{1680}(1409, \cdot)\) None 0 2
1680.1.dt \(\chi_{1680}(409, \cdot)\) None 0 2
1680.1.dy \(\chi_{1680}(79, \cdot)\) None 0 2
1680.1.dz \(\chi_{1680}(1319, \cdot)\) None 0 2
1680.1.ec \(\chi_{1680}(311, \cdot)\) None 0 2
1680.1.ed \(\chi_{1680}(751, \cdot)\) None 0 2
1680.1.ee \(\chi_{1680}(1081, \cdot)\) None 0 2
1680.1.ef \(\chi_{1680}(401, \cdot)\) None 0 2
1680.1.ek \(\chi_{1680}(103, \cdot)\) None 0 4
1680.1.el \(\chi_{1680}(527, \cdot)\) None 0 4
1680.1.em \(\chi_{1680}(193, \cdot)\) None 0 4
1680.1.en \(\chi_{1680}(857, \cdot)\) None 0 4
1680.1.er \(\chi_{1680}(283, \cdot)\) None 0 4
1680.1.es \(\chi_{1680}(37, \cdot)\) None 0 4
1680.1.eu \(\chi_{1680}(773, \cdot)\) None 0 4
1680.1.ex \(\chi_{1680}(107, \cdot)\) None 0 4
1680.1.ez \(\chi_{1680}(331, \cdot)\) None 0 4
1680.1.fa \(\chi_{1680}(229, \cdot)\) None 0 4
1680.1.fd \(\chi_{1680}(131, \cdot)\) None 0 4
1680.1.fe \(\chi_{1680}(149, \cdot)\) None 0 4
1680.1.fg \(\chi_{1680}(59, \cdot)\) None 0 4
1680.1.fj \(\chi_{1680}(221, \cdot)\) None 0 4
1680.1.fk \(\chi_{1680}(499, \cdot)\) None 0 4
1680.1.fn \(\chi_{1680}(61, \cdot)\) None 0 4
1680.1.fo \(\chi_{1680}(373, \cdot)\) None 0 4
1680.1.fr \(\chi_{1680}(187, \cdot)\) None 0 4
1680.1.ft \(\chi_{1680}(443, \cdot)\) None 0 4
1680.1.fu \(\chi_{1680}(173, \cdot)\) None 0 4
1680.1.fy \(\chi_{1680}(457, \cdot)\) None 0 4
1680.1.fz \(\chi_{1680}(17, \cdot)\) None 0 4
1680.1.ga \(\chi_{1680}(367, \cdot)\) None 0 4
1680.1.gb \(\chi_{1680}(23, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1680))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1680)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 2}\)