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Properties

Label 960.3.ce
Level $960$
Weight $3$
Character orbit 960.ce
Rep. character $\chi_{960}(133,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1536$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 960.ce (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(960, [\chi])\).

Total New Old
Modular forms 3104 1536 1568
Cusp forms 3040 1536 1504
Eisenstein series 64 0 64

Trace form

\( 1536 q + O(q^{10}) \) \( 1536 q + 96 q^{12} + 64 q^{14} + 224 q^{22} + 144 q^{24} + 272 q^{40} - 384 q^{51} + 1344 q^{56} + 704 q^{58} - 288 q^{66} + 1232 q^{68} + 384 q^{69} + 1024 q^{71} - 208 q^{76} + 512 q^{79} - 1520 q^{82} - 1584 q^{88} + 1872 q^{92} + 912 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(960, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)