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Properties

Label 1920.1
Level 1920
Weight 1
Dimension 64
Nonzero newspaces 5
Newform subspaces 12
Sturm bound 196608
Trace bound 49

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Defining parameters

Level: \( N \) = \( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 12 \)
Sturm bound: \(196608\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1920))\).

Total New Old
Modular forms 2824 352 2472
Cusp forms 264 64 200
Eisenstein series 2560 288 2272

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 64 0 0 0

Trace form

\( 64 q + 8 q^{25} - 8 q^{33} - 16 q^{49} - 8 q^{51} - 32 q^{54} - 16 q^{61} - 16 q^{69} + 8 q^{73} - 32 q^{76} - 8 q^{81} + 8 q^{85} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1920))\)

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
1920.1.c \(\chi_{1920}(1409, \cdot)\) None 0 1
1920.1.e \(\chi_{1920}(511, \cdot)\) None 0 1
1920.1.g \(\chi_{1920}(1471, \cdot)\) None 0 1
1920.1.i \(\chi_{1920}(449, \cdot)\) 1920.1.i.a 1 1
1920.1.i.b 1
1920.1.i.c 1
1920.1.i.d 1
1920.1.i.e 2
1920.1.i.f 2
1920.1.j \(\chi_{1920}(1279, \cdot)\) None 0 1
1920.1.l \(\chi_{1920}(641, \cdot)\) None 0 1
1920.1.n \(\chi_{1920}(1601, \cdot)\) None 0 1
1920.1.p \(\chi_{1920}(319, \cdot)\) None 0 1
1920.1.q \(\chi_{1920}(799, \cdot)\) None 0 2
1920.1.r \(\chi_{1920}(161, \cdot)\) None 0 2
1920.1.u \(\chi_{1920}(1343, \cdot)\) 1920.1.u.a 4 2
1920.1.u.b 4
1920.1.x \(\chi_{1920}(193, \cdot)\) None 0 2
1920.1.z \(\chi_{1920}(287, \cdot)\) None 0 2
1920.1.ba \(\chi_{1920}(97, \cdot)\) None 0 2
1920.1.bd \(\chi_{1920}(1247, \cdot)\) None 0 2
1920.1.be \(\chi_{1920}(1057, \cdot)\) None 0 2
1920.1.bg \(\chi_{1920}(1153, \cdot)\) None 0 2
1920.1.bj \(\chi_{1920}(383, \cdot)\) None 0 2
1920.1.bm \(\chi_{1920}(929, \cdot)\) 1920.1.bm.a 4 2
1920.1.bm.b 4
1920.1.bn \(\chi_{1920}(31, \cdot)\) None 0 2
1920.1.bp \(\chi_{1920}(817, \cdot)\) None 0 4
1920.1.bq \(\chi_{1920}(47, \cdot)\) None 0 4
1920.1.bt \(\chi_{1920}(271, \cdot)\) None 0 4
1920.1.bu \(\chi_{1920}(209, \cdot)\) 1920.1.bu.a 8 4
1920.1.bw \(\chi_{1920}(79, \cdot)\) None 0 4
1920.1.bz \(\chi_{1920}(401, \cdot)\) None 0 4
1920.1.ca \(\chi_{1920}(527, \cdot)\) None 0 4
1920.1.cd \(\chi_{1920}(337, \cdot)\) None 0 4
1920.1.ce \(\chi_{1920}(313, \cdot)\) None 0 8
1920.1.ch \(\chi_{1920}(23, \cdot)\) None 0 8
1920.1.cj \(\chi_{1920}(41, \cdot)\) None 0 8
1920.1.cl \(\chi_{1920}(89, \cdot)\) None 0 8
1920.1.cm \(\chi_{1920}(151, \cdot)\) None 0 8
1920.1.co \(\chi_{1920}(199, \cdot)\) None 0 8
1920.1.cq \(\chi_{1920}(73, \cdot)\) None 0 8
1920.1.ct \(\chi_{1920}(263, \cdot)\) None 0 8
1920.1.cu \(\chi_{1920}(13, \cdot)\) None 0 16
1920.1.cv \(\chi_{1920}(83, \cdot)\) None 0 16
1920.1.da \(\chi_{1920}(91, \cdot)\) None 0 16
1920.1.db \(\chi_{1920}(29, \cdot)\) 1920.1.db.a 32 16
1920.1.de \(\chi_{1920}(101, \cdot)\) None 0 16
1920.1.df \(\chi_{1920}(19, \cdot)\) None 0 16
1920.1.dg \(\chi_{1920}(203, \cdot)\) None 0 16
1920.1.dh \(\chi_{1920}(133, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1920))\) into lower level spaces

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