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Properties

Label 2304.3.u
Level $2304$
Weight $3$
Character orbit 2304.u
Rep. character $\chi_{2304}(415,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $312$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2304.u (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2304, [\chi])\).

Total New Old
Modular forms 3200 328 2872
Cusp forms 2944 312 2632
Eisenstein series 256 16 240

Trace form

\( 312 q - 8 q^{5} + O(q^{10}) \) \( 312 q - 8 q^{5} + 8 q^{13} - 8 q^{25} - 8 q^{29} + 8 q^{37} + 8 q^{41} + 312 q^{53} - 120 q^{61} + 16 q^{65} - 8 q^{73} - 456 q^{77} - 192 q^{85} + 8 q^{89} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

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