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Properties

Label 960.1
Level 960
Weight 1
Dimension 32
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 49152
Trace bound 15

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Defining parameters

Level: \( N \) = \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(49152\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(960))\).

Total New Old
Modular forms 1256 164 1092
Cusp forms 104 32 72
Eisenstein series 1152 132 1020

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32 q + O(q^{10}) \) \( 32 q + 4 q^{15} + 4 q^{19} - 4 q^{21} - 4 q^{25} + 8 q^{33} + 4 q^{45} - 8 q^{49} - 20 q^{51} + 16 q^{54} + 4 q^{61} + 8 q^{69} - 8 q^{73} + 16 q^{76} - 24 q^{79} - 16 q^{81} - 4 q^{85} - 16 q^{94} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(960))\)

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
960.1.c \(\chi_{960}(449, \cdot)\) 960.1.c.a 4 1
960.1.e \(\chi_{960}(511, \cdot)\) None 0 1
960.1.g \(\chi_{960}(31, \cdot)\) None 0 1
960.1.i \(\chi_{960}(929, \cdot)\) None 0 1
960.1.j \(\chi_{960}(319, \cdot)\) None 0 1
960.1.l \(\chi_{960}(641, \cdot)\) None 0 1
960.1.n \(\chi_{960}(161, \cdot)\) None 0 1
960.1.p \(\chi_{960}(799, \cdot)\) None 0 1
960.1.q \(\chi_{960}(79, \cdot)\) None 0 2
960.1.r \(\chi_{960}(401, \cdot)\) None 0 2
960.1.u \(\chi_{960}(287, \cdot)\) 960.1.u.a 4 2
960.1.u.b 4
960.1.x \(\chi_{960}(97, \cdot)\) None 0 2
960.1.z \(\chi_{960}(527, \cdot)\) None 0 2
960.1.ba \(\chi_{960}(817, \cdot)\) None 0 2
960.1.bd \(\chi_{960}(47, \cdot)\) None 0 2
960.1.be \(\chi_{960}(337, \cdot)\) None 0 2
960.1.bg \(\chi_{960}(193, \cdot)\) None 0 2
960.1.bj \(\chi_{960}(383, \cdot)\) None 0 2
960.1.bm \(\chi_{960}(209, \cdot)\) 960.1.bm.a 4 2
960.1.bn \(\chi_{960}(271, \cdot)\) None 0 2
960.1.bp \(\chi_{960}(73, \cdot)\) None 0 4
960.1.bq \(\chi_{960}(263, \cdot)\) None 0 4
960.1.bt \(\chi_{960}(151, \cdot)\) None 0 4
960.1.bu \(\chi_{960}(89, \cdot)\) None 0 4
960.1.bw \(\chi_{960}(199, \cdot)\) None 0 4
960.1.bz \(\chi_{960}(41, \cdot)\) None 0 4
960.1.ca \(\chi_{960}(23, \cdot)\) None 0 4
960.1.cd \(\chi_{960}(313, \cdot)\) None 0 4
960.1.ce \(\chi_{960}(133, \cdot)\) None 0 8
960.1.ch \(\chi_{960}(83, \cdot)\) None 0 8
960.1.cj \(\chi_{960}(101, \cdot)\) None 0 8
960.1.cl \(\chi_{960}(29, \cdot)\) 960.1.cl.a 16 8
960.1.cm \(\chi_{960}(91, \cdot)\) None 0 8
960.1.co \(\chi_{960}(19, \cdot)\) None 0 8
960.1.cq \(\chi_{960}(13, \cdot)\) None 0 8
960.1.ct \(\chi_{960}(203, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(960))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(960)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)