Properties

Label 960.4.v
Level $960$
Weight $4$
Character orbit 960.v
Rep. character $\chi_{960}(257,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
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.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1200 296 904
Cusp forms 1104 280 824
Eisenstein series 96 16 80

Trace form

\( 280 q + O(q^{10}) \) \( 280 q + 8 q^{13} + 8 q^{21} - 8 q^{25} + 104 q^{33} + 8 q^{37} + 504 q^{45} + 104 q^{57} - 1808 q^{61} - 8 q^{73} + 2456 q^{81} + 8 q^{85} + 5056 q^{93} + 2968 q^{97} + O(q^{100}) \)

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)