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Properties

Label 960.3.cm
Level $960$
Weight $3$
Character orbit 960.cm
Rep. character $\chi_{960}(91,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1024$
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.cm (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
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 1024 2080
Cusp forms 3040 1024 2016
Eisenstein series 64 0 64

Trace form

\( 1024 q + O(q^{10}) \) \( 1024 q - 288 q^{22} - 480 q^{28} + 160 q^{32} + 480 q^{34} + 1120 q^{38} + 416 q^{44} - 384 q^{51} + 1056 q^{52} + 144 q^{54} + 224 q^{56} - 512 q^{59} + 192 q^{62} - 96 q^{64} - 288 q^{66} + 256 q^{67} - 960 q^{68} + 1024 q^{71} - 352 q^{74} - 208 q^{76} - 1440 q^{78} + 512 q^{79} - 1120 q^{88} - 16 q^{94} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)