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Properties

Label 3840.1
Level 3840
Weight 1
Dimension 132
Nonzero newspaces 6
Newform subspaces 18
Sturm bound 786432
Trace bound 61

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Defining parameters

Level: \( N \) = \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 18 \)
Sturm bound: \(786432\)
Trace bound: \(61\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3840))\).

Total New Old
Modular forms 6248 756 5492
Cusp forms 616 132 484
Eisenstein series 5632 624 5008

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 132 0 0 0

Trace form

\( 132 q + 4 q^{9} + 4 q^{25} - 12 q^{49} + 16 q^{51} + 16 q^{61} + 16 q^{69} + 16 q^{79} - 12 q^{81} - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3840))\)

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
3840.1.c \(\chi_{3840}(3329, \cdot)\) 3840.1.c.a 1 1
3840.1.c.b 1
3840.1.c.c 1
3840.1.c.d 1
3840.1.c.e 2
3840.1.c.f 2
3840.1.c.g 2
3840.1.c.h 2
3840.1.e \(\chi_{3840}(511, \cdot)\) None 0 1
3840.1.g \(\chi_{3840}(2431, \cdot)\) None 0 1
3840.1.i \(\chi_{3840}(1409, \cdot)\) 3840.1.i.a 4 1
3840.1.i.b 4
3840.1.j \(\chi_{3840}(1279, \cdot)\) None 0 1
3840.1.l \(\chi_{3840}(2561, \cdot)\) None 0 1
3840.1.n \(\chi_{3840}(641, \cdot)\) None 0 1
3840.1.p \(\chi_{3840}(3199, \cdot)\) None 0 1
3840.1.q \(\chi_{3840}(319, \cdot)\) None 0 2
3840.1.r \(\chi_{3840}(1601, \cdot)\) None 0 2
3840.1.u \(\chi_{3840}(383, \cdot)\) None 0 2
3840.1.x \(\chi_{3840}(1153, \cdot)\) None 0 2
3840.1.z \(\chi_{3840}(3263, \cdot)\) None 0 2
3840.1.ba \(\chi_{3840}(2113, \cdot)\) None 0 2
3840.1.bd \(\chi_{3840}(1343, \cdot)\) None 0 2
3840.1.be \(\chi_{3840}(193, \cdot)\) None 0 2
3840.1.bg \(\chi_{3840}(1537, \cdot)\) None 0 2
3840.1.bj \(\chi_{3840}(767, \cdot)\) 3840.1.bj.a 4 2
3840.1.bj.b 4
3840.1.bj.c 4
3840.1.bj.d 4
3840.1.bm \(\chi_{3840}(449, \cdot)\) None 0 2
3840.1.bn \(\chi_{3840}(1471, \cdot)\) None 0 2
3840.1.bp \(\chi_{3840}(97, \cdot)\) None 0 4
3840.1.bq \(\chi_{3840}(1247, \cdot)\) None 0 4
3840.1.bt \(\chi_{3840}(31, \cdot)\) None 0 4
3840.1.bu \(\chi_{3840}(929, \cdot)\) 3840.1.bu.a 8 4
3840.1.bu.b 8
3840.1.bw \(\chi_{3840}(799, \cdot)\) None 0 4
3840.1.bz \(\chi_{3840}(161, \cdot)\) None 0 4
3840.1.ca \(\chi_{3840}(287, \cdot)\) None 0 4
3840.1.cd \(\chi_{3840}(1057, \cdot)\) None 0 4
3840.1.ce \(\chi_{3840}(337, \cdot)\) None 0 8
3840.1.ch \(\chi_{3840}(527, \cdot)\) None 0 8
3840.1.cj \(\chi_{3840}(401, \cdot)\) None 0 8
3840.1.cl \(\chi_{3840}(209, \cdot)\) 3840.1.cl.a 16 8
3840.1.cm \(\chi_{3840}(271, \cdot)\) None 0 8
3840.1.co \(\chi_{3840}(79, \cdot)\) None 0 8
3840.1.cq \(\chi_{3840}(817, \cdot)\) None 0 8
3840.1.ct \(\chi_{3840}(47, \cdot)\) None 0 8
3840.1.cu \(\chi_{3840}(73, \cdot)\) None 0 16
3840.1.cv \(\chi_{3840}(23, \cdot)\) None 0 16
3840.1.da \(\chi_{3840}(151, \cdot)\) None 0 16
3840.1.db \(\chi_{3840}(89, \cdot)\) None 0 16
3840.1.de \(\chi_{3840}(41, \cdot)\) None 0 16
3840.1.df \(\chi_{3840}(199, \cdot)\) None 0 16
3840.1.dg \(\chi_{3840}(263, \cdot)\) None 0 16
3840.1.dh \(\chi_{3840}(313, \cdot)\) None 0 16
3840.1.dk \(\chi_{3840}(19, \cdot)\) None 0 32
3840.1.dl \(\chi_{3840}(101, \cdot)\) None 0 32
3840.1.dp \(\chi_{3840}(203, \cdot)\) None 0 32
3840.1.dq \(\chi_{3840}(133, \cdot)\) None 0 32
3840.1.dt \(\chi_{3840}(83, \cdot)\) None 0 32
3840.1.du \(\chi_{3840}(13, \cdot)\) None 0 32
3840.1.dy \(\chi_{3840}(29, \cdot)\) 3840.1.dy.a 64 32
3840.1.dz \(\chi_{3840}(91, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3840))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3840)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 28}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1920))\)\(^{\oplus 2}\)