Properties

Label 2304.3.n
Level $2304$
Weight $3$
Character orbit 2304.n
Rep. character $\chi_{2304}(641,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2304.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1584 392 1192
Cusp forms 1488 376 1112
Eisenstein series 96 16 80

Trace form

\( 376q + 8q^{9} + O(q^{10}) \) \( 376q + 8q^{9} - 856q^{25} - 44q^{33} + 12q^{41} - 1152q^{49} + 80q^{57} - 12q^{65} + 16q^{73} - 8q^{81} - 4q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)