Properties

Label 3360.1
Level 3360
Weight 1
Dimension 80
Nonzero newspaces 5
Newform subspaces 14
Sturm bound 589824
Trace bound 21

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Defining parameters

Level: \( N \) = \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 14 \)
Sturm bound: \(589824\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3360))\).

Total New Old
Modular forms 6856 680 6176
Cusp forms 712 80 632
Eisenstein series 6144 600 5544

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 80 0 0 0

Trace form

\( 80q + 4q^{9} + O(q^{10}) \) \( 80q + 4q^{9} + 4q^{15} - 4q^{21} + 6q^{25} + 4q^{31} - 12q^{33} - 4q^{45} - 4q^{49} - 12q^{55} + 8q^{57} - 4q^{63} - 16q^{69} - 4q^{79} - 24q^{81} - 12q^{87} - 16q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3360))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3360.1.b \(\chi_{3360}(1679, \cdot)\) None 0 1
3360.1.c \(\chi_{3360}(799, \cdot)\) None 0 1
3360.1.h \(\chi_{3360}(2449, \cdot)\) None 0 1
3360.1.i \(\chi_{3360}(449, \cdot)\) None 0 1
3360.1.l \(\chi_{3360}(1121, \cdot)\) None 0 1
3360.1.m \(\chi_{3360}(3121, \cdot)\) None 0 1
3360.1.n \(\chi_{3360}(1471, \cdot)\) None 0 1
3360.1.o \(\chi_{3360}(2351, \cdot)\) None 0 1
3360.1.r \(\chi_{3360}(2801, \cdot)\) None 0 1
3360.1.s \(\chi_{3360}(1441, \cdot)\) None 0 1
3360.1.x \(\chi_{3360}(3151, \cdot)\) None 0 1
3360.1.y \(\chi_{3360}(671, \cdot)\) None 0 1
3360.1.bb \(\chi_{3360}(3359, \cdot)\) None 0 1
3360.1.bc \(\chi_{3360}(2479, \cdot)\) None 0 1
3360.1.bd \(\chi_{3360}(769, \cdot)\) None 0 1
3360.1.be \(\chi_{3360}(2129, \cdot)\) None 0 1
3360.1.bh \(\chi_{3360}(1583, \cdot)\) None 0 2
3360.1.bi \(\chi_{3360}(223, \cdot)\) None 0 2
3360.1.bn \(\chi_{3360}(1217, \cdot)\) 3360.1.bn.a 4 2
3360.1.bn.b 4
3360.1.bn.c 4
3360.1.bn.d 4
3360.1.bo \(\chi_{3360}(337, \cdot)\) None 0 2
3360.1.bq \(\chi_{3360}(2087, \cdot)\) None 0 2
3360.1.br \(\chi_{3360}(2057, \cdot)\) None 0 2
3360.1.bt \(\chi_{3360}(1177, \cdot)\) None 0 2
3360.1.bw \(\chi_{3360}(727, \cdot)\) None 0 2
3360.1.by \(\chi_{3360}(1639, \cdot)\) None 0 2
3360.1.bz \(\chi_{3360}(601, \cdot)\) None 0 2
3360.1.cc \(\chi_{3360}(839, \cdot)\) None 0 2
3360.1.cd \(\chi_{3360}(281, \cdot)\) None 0 2
3360.1.cf \(\chi_{3360}(1511, \cdot)\) None 0 2
3360.1.ci \(\chi_{3360}(1289, \cdot)\) None 0 2
3360.1.cj \(\chi_{3360}(631, \cdot)\) None 0 2
3360.1.cm \(\chi_{3360}(1609, \cdot)\) None 0 2
3360.1.cn \(\chi_{3360}(377, \cdot)\) None 0 2
3360.1.cq \(\chi_{3360}(407, \cdot)\) None 0 2
3360.1.cs \(\chi_{3360}(2407, \cdot)\) None 0 2
3360.1.ct \(\chi_{3360}(2857, \cdot)\) None 0 2
3360.1.cv \(\chi_{3360}(1553, \cdot)\) 3360.1.cv.a 4 2
3360.1.cv.b 4
3360.1.cv.c 8
3360.1.cv.d 8
3360.1.cw \(\chi_{3360}(673, \cdot)\) None 0 2
3360.1.db \(\chi_{3360}(1247, \cdot)\) None 0 2
3360.1.dc \(\chi_{3360}(1903, \cdot)\) None 0 2
3360.1.dd \(\chi_{3360}(1151, \cdot)\) None 0 2
3360.1.de \(\chi_{3360}(751, \cdot)\) None 0 2
3360.1.dj \(\chi_{3360}(481, \cdot)\) None 0 2
3360.1.dk \(\chi_{3360}(401, \cdot)\) None 0 2
3360.1.dm \(\chi_{3360}(1649, \cdot)\) 3360.1.dm.a 4 2
3360.1.dm.b 4
3360.1.dn \(\chi_{3360}(1249, \cdot)\) None 0 2
3360.1.do \(\chi_{3360}(79, \cdot)\) None 0 2
3360.1.dp \(\chi_{3360}(479, \cdot)\) None 0 2
3360.1.ds \(\chi_{3360}(1409, \cdot)\) 3360.1.ds.a 8 2
3360.1.ds.b 8
3360.1.dt \(\chi_{3360}(1489, \cdot)\) None 0 2
3360.1.dy \(\chi_{3360}(319, \cdot)\) None 0 2
3360.1.dz \(\chi_{3360}(719, \cdot)\) None 0 2
3360.1.ec \(\chi_{3360}(1391, \cdot)\) None 0 2
3360.1.ed \(\chi_{3360}(991, \cdot)\) None 0 2
3360.1.ee \(\chi_{3360}(241, \cdot)\) None 0 2
3360.1.ef \(\chi_{3360}(641, \cdot)\) None 0 2
3360.1.ej \(\chi_{3360}(349, \cdot)\) None 0 4
3360.1.el \(\chi_{3360}(211, \cdot)\) None 0 4
3360.1.em \(\chi_{3360}(29, \cdot)\) None 0 4
3360.1.eo \(\chi_{3360}(251, \cdot)\) None 0 4
3360.1.eq \(\chi_{3360}(323, \cdot)\) None 0 4
3360.1.er \(\chi_{3360}(293, \cdot)\) None 0 4
3360.1.eu \(\chi_{3360}(307, \cdot)\) None 0 4
3360.1.ev \(\chi_{3360}(253, \cdot)\) None 0 4
3360.1.fa \(\chi_{3360}(1163, \cdot)\) None 0 4
3360.1.fb \(\chi_{3360}(1133, \cdot)\) None 0 4
3360.1.fe \(\chi_{3360}(643, \cdot)\) None 0 4
3360.1.ff \(\chi_{3360}(1093, \cdot)\) None 0 4
3360.1.fg \(\chi_{3360}(379, \cdot)\) None 0 4
3360.1.fi \(\chi_{3360}(181, \cdot)\) None 0 4
3360.1.fl \(\chi_{3360}(419, \cdot)\) None 0 4
3360.1.fn \(\chi_{3360}(701, \cdot)\) None 0 4
3360.1.fq \(\chi_{3360}(367, \cdot)\) None 0 4
3360.1.fr \(\chi_{3360}(767, \cdot)\) None 0 4
3360.1.fs \(\chi_{3360}(193, \cdot)\) None 0 4
3360.1.ft \(\chi_{3360}(17, \cdot)\) 3360.1.ft.a 8 4
3360.1.ft.b 8
3360.1.fx \(\chi_{3360}(103, \cdot)\) None 0 4
3360.1.fy \(\chi_{3360}(697, \cdot)\) None 0 4
3360.1.ga \(\chi_{3360}(1097, \cdot)\) None 0 4
3360.1.gd \(\chi_{3360}(23, \cdot)\) None 0 4
3360.1.gf \(\chi_{3360}(151, \cdot)\) None 0 4
3360.1.gg \(\chi_{3360}(409, \cdot)\) None 0 4
3360.1.gj \(\chi_{3360}(311, \cdot)\) None 0 4
3360.1.gk \(\chi_{3360}(569, \cdot)\) None 0 4
3360.1.gm \(\chi_{3360}(1319, \cdot)\) None 0 4
3360.1.gp \(\chi_{3360}(1241, \cdot)\) None 0 4
3360.1.gq \(\chi_{3360}(919, \cdot)\) None 0 4
3360.1.gt \(\chi_{3360}(1081, \cdot)\) None 0 4
3360.1.gu \(\chi_{3360}(457, \cdot)\) None 0 4
3360.1.gx \(\chi_{3360}(1447, \cdot)\) None 0 4
3360.1.gz \(\chi_{3360}(263, \cdot)\) None 0 4
3360.1.ha \(\chi_{3360}(857, \cdot)\) None 0 4
3360.1.he \(\chi_{3360}(1297, \cdot)\) None 0 4
3360.1.hf \(\chi_{3360}(257, \cdot)\) None 0 4
3360.1.hg \(\chi_{3360}(607, \cdot)\) None 0 4
3360.1.hh \(\chi_{3360}(527, \cdot)\) None 0 4
3360.1.hl \(\chi_{3360}(221, \cdot)\) None 0 8
3360.1.hn \(\chi_{3360}(59, \cdot)\) None 0 8
3360.1.ho \(\chi_{3360}(61, \cdot)\) None 0 8
3360.1.hq \(\chi_{3360}(499, \cdot)\) None 0 8
3360.1.hs \(\chi_{3360}(373, \cdot)\) None 0 8
3360.1.ht \(\chi_{3360}(187, \cdot)\) None 0 8
3360.1.hw \(\chi_{3360}(173, \cdot)\) None 0 8
3360.1.hx \(\chi_{3360}(443, \cdot)\) None 0 8
3360.1.ic \(\chi_{3360}(37, \cdot)\) None 0 8
3360.1.id \(\chi_{3360}(283, \cdot)\) None 0 8
3360.1.ig \(\chi_{3360}(773, \cdot)\) None 0 8
3360.1.ih \(\chi_{3360}(107, \cdot)\) None 0 8
3360.1.ii \(\chi_{3360}(131, \cdot)\) None 0 8
3360.1.ik \(\chi_{3360}(149, \cdot)\) None 0 8
3360.1.in \(\chi_{3360}(331, \cdot)\) None 0 8
3360.1.ip \(\chi_{3360}(229, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3360))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3360)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1680))\)\(^{\oplus 2}\)