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Properties

Label 2304.4.v
Level $2304$
Weight $4$
Character orbit 2304.v
Rep. character $\chi_{2304}(289,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $472$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2304.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2304, [\chi])\).

Total New Old
Modular forms 4736 488 4248
Cusp forms 4480 472 4008
Eisenstein series 256 16 240

Trace form

\( 472 q - 8 q^{5} + O(q^{10}) \) \( 472 q - 8 q^{5} + 8 q^{13} - 8 q^{25} - 8 q^{29} + 8 q^{37} + 8 q^{41} - 1512 q^{53} - 3640 q^{61} + 16 q^{65} - 8 q^{73} - 3816 q^{77} - 992 q^{85} + 8 q^{89} - 16 q^{97} + O(q^{100}) \)

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Decomposition of \(S_{4}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)