Properties

Label 2880.1
Level 2880
Weight 1
Dimension 69
Nonzero newspaces 10
Newform subspaces 18
Sturm bound 442368
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 18 \)
Sturm bound: \(442368\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2880))\).

Total New Old
Modular forms 5132 663 4469
Cusp forms 524 69 455
Eisenstein series 4608 594 4014

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 69 0 0 0

Trace form

\( 69 q - q^{5} + O(q^{10}) \) \( 69 q - q^{5} - 2 q^{13} + 2 q^{17} - 4 q^{19} + 8 q^{21} - 11 q^{25} + 10 q^{29} + 2 q^{37} + 2 q^{41} - 7 q^{49} + 2 q^{53} + 10 q^{61} - 2 q^{65} - 2 q^{73} - 16 q^{76} + 16 q^{79} + 2 q^{85} - 10 q^{89} - 16 q^{94} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2880))\)

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
2880.1.c \(\chi_{2880}(449, \cdot)\) 2880.1.c.a 4 1
2880.1.e \(\chi_{2880}(2431, \cdot)\) None 0 1
2880.1.g \(\chi_{2880}(991, \cdot)\) None 0 1
2880.1.i \(\chi_{2880}(1889, \cdot)\) 2880.1.i.a 4 1
2880.1.i.b 4
2880.1.j \(\chi_{2880}(1279, \cdot)\) 2880.1.j.a 1 1
2880.1.j.b 2
2880.1.l \(\chi_{2880}(1601, \cdot)\) None 0 1
2880.1.n \(\chi_{2880}(161, \cdot)\) None 0 1
2880.1.p \(\chi_{2880}(2719, \cdot)\) 2880.1.p.a 2 1
2880.1.p.b 2
2880.1.r \(\chi_{2880}(559, \cdot)\) 2880.1.r.a 4 2
2880.1.s \(\chi_{2880}(881, \cdot)\) None 0 2
2880.1.v \(\chi_{2880}(287, \cdot)\) None 0 2
2880.1.y \(\chi_{2880}(2017, \cdot)\) None 0 2
2880.1.ba \(\chi_{2880}(1583, \cdot)\) None 0 2
2880.1.bb \(\chi_{2880}(1873, \cdot)\) None 0 2
2880.1.be \(\chi_{2880}(143, \cdot)\) None 0 2
2880.1.bf \(\chi_{2880}(433, \cdot)\) None 0 2
2880.1.bh \(\chi_{2880}(577, \cdot)\) 2880.1.bh.a 2 2
2880.1.bh.b 2
2880.1.bh.c 2
2880.1.bk \(\chi_{2880}(1727, \cdot)\) 2880.1.bk.a 4 2
2880.1.bk.b 4
2880.1.bn \(\chi_{2880}(1169, \cdot)\) None 0 2
2880.1.bo \(\chi_{2880}(271, \cdot)\) None 0 2
2880.1.bp \(\chi_{2880}(799, \cdot)\) None 0 2
2880.1.bq \(\chi_{2880}(1121, \cdot)\) None 0 2
2880.1.bs \(\chi_{2880}(641, \cdot)\) None 0 2
2880.1.bu \(\chi_{2880}(319, \cdot)\) 2880.1.bu.a 2 2
2880.1.bu.b 2
2880.1.bu.c 4
2880.1.bx \(\chi_{2880}(929, \cdot)\) None 0 2
2880.1.bz \(\chi_{2880}(31, \cdot)\) None 0 2
2880.1.cb \(\chi_{2880}(511, \cdot)\) None 0 2
2880.1.cd \(\chi_{2880}(1409, \cdot)\) 2880.1.cd.a 8 2
2880.1.cf \(\chi_{2880}(73, \cdot)\) None 0 4
2880.1.cg \(\chi_{2880}(1223, \cdot)\) None 0 4
2880.1.cj \(\chi_{2880}(631, \cdot)\) None 0 4
2880.1.ck \(\chi_{2880}(89, \cdot)\) None 0 4
2880.1.cm \(\chi_{2880}(199, \cdot)\) None 0 4
2880.1.cp \(\chi_{2880}(521, \cdot)\) None 0 4
2880.1.cq \(\chi_{2880}(503, \cdot)\) None 0 4
2880.1.ct \(\chi_{2880}(793, \cdot)\) None 0 4
2880.1.cw \(\chi_{2880}(751, \cdot)\) None 0 4
2880.1.cx \(\chi_{2880}(209, \cdot)\) None 0 4
2880.1.cz \(\chi_{2880}(193, \cdot)\) None 0 4
2880.1.da \(\chi_{2880}(383, \cdot)\) None 0 4
2880.1.dd \(\chi_{2880}(337, \cdot)\) None 0 4
2880.1.de \(\chi_{2880}(47, \cdot)\) None 0 4
2880.1.dh \(\chi_{2880}(817, \cdot)\) None 0 4
2880.1.di \(\chi_{2880}(527, \cdot)\) None 0 4
2880.1.dl \(\chi_{2880}(1247, \cdot)\) None 0 4
2880.1.dm \(\chi_{2880}(97, \cdot)\) None 0 4
2880.1.do \(\chi_{2880}(401, \cdot)\) None 0 4
2880.1.dp \(\chi_{2880}(79, \cdot)\) None 0 4
2880.1.ds \(\chi_{2880}(397, \cdot)\) None 0 8
2880.1.dv \(\chi_{2880}(107, \cdot)\) None 0 8
2880.1.dx \(\chi_{2880}(341, \cdot)\) None 0 8
2880.1.dz \(\chi_{2880}(269, \cdot)\) None 0 8
2880.1.ea \(\chi_{2880}(91, \cdot)\) None 0 8
2880.1.ec \(\chi_{2880}(19, \cdot)\) 2880.1.ec.a 16 8
2880.1.ee \(\chi_{2880}(37, \cdot)\) None 0 8
2880.1.eh \(\chi_{2880}(467, \cdot)\) None 0 8
2880.1.ei \(\chi_{2880}(313, \cdot)\) None 0 8
2880.1.el \(\chi_{2880}(23, \cdot)\) None 0 8
2880.1.en \(\chi_{2880}(329, \cdot)\) None 0 8
2880.1.eo \(\chi_{2880}(151, \cdot)\) None 0 8
2880.1.eq \(\chi_{2880}(41, \cdot)\) None 0 8
2880.1.et \(\chi_{2880}(439, \cdot)\) None 0 8
2880.1.ev \(\chi_{2880}(263, \cdot)\) None 0 8
2880.1.ew \(\chi_{2880}(553, \cdot)\) None 0 8
2880.1.ez \(\chi_{2880}(83, \cdot)\) None 0 16
2880.1.fa \(\chi_{2880}(133, \cdot)\) None 0 16
2880.1.fc \(\chi_{2880}(139, \cdot)\) None 0 16
2880.1.fe \(\chi_{2880}(211, \cdot)\) None 0 16
2880.1.fh \(\chi_{2880}(29, \cdot)\) None 0 16
2880.1.fj \(\chi_{2880}(101, \cdot)\) None 0 16
2880.1.fl \(\chi_{2880}(203, \cdot)\) None 0 16
2880.1.fm \(\chi_{2880}(13, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2880))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2880)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1440))\)\(^{\oplus 2}\)