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Properties

Label 960.4.cr
Level $960$
Weight $4$
Character orbit 960.cr
Rep. character $\chi_{960}(53,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $4576$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 960.cr (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 960 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(960, [\chi])\).

Total New Old
Modular forms 4640 4640 0
Cusp forms 4576 4576 0
Eisenstein series 64 64 0

Trace form

\( 4576 q - 8 q^{3} - 16 q^{6} - 16 q^{7} + O(q^{10}) \) \( 4576 q - 8 q^{3} - 16 q^{6} - 16 q^{7} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 32 q^{16} - 8 q^{18} - 16 q^{21} + 848 q^{22} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 2264 q^{30} - 256 q^{34} - 16 q^{36} - 16 q^{37} - 592 q^{40} - 8 q^{42} - 16 q^{43} - 8 q^{45} - 32 q^{46} - 4896 q^{48} - 16 q^{51} - 16 q^{52} - 16 q^{55} - 8 q^{57} - 4048 q^{58} - 6112 q^{60} - 32 q^{61} - 16 q^{63} - 16 q^{66} - 16 q^{67} - 16 q^{70} - 2768 q^{72} - 16 q^{73} - 8 q^{75} - 10448 q^{76} - 11712 q^{78} + 5664 q^{79} - 16 q^{81} - 6976 q^{82} - 2016 q^{85} + 2568 q^{87} - 16 q^{88} - 8 q^{90} - 32 q^{91} + 208 q^{93} - 256 q^{94} - 16 q^{96} + 10624 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.