Properties

Label 2304.2.bj
Level $2304$
Weight $2$
Character orbit 2304.bj
Rep. character $\chi_{2304}(95,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $736$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.bj (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 288 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2304, [\chi])\).

Total New Old
Modular forms 3200 800 2400
Cusp forms 2944 736 2208
Eisenstein series 256 64 192

Trace form

\( 736q + 24q^{5} - 16q^{9} + O(q^{10}) \) \( 736q + 24q^{5} - 16q^{9} + 8q^{13} + 16q^{21} - 8q^{25} + 24q^{29} - 32q^{33} + 32q^{37} - 24q^{41} + 16q^{45} - 16q^{57} + 8q^{61} - 48q^{65} + 16q^{69} - 32q^{73} + 24q^{77} + 48q^{85} + 40q^{93} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database