Properties

Label 2304.4.bq
Level $2304$
Weight $4$
Character orbit 2304.bq
Rep. character $\chi_{2304}(49,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $4576$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2304.bq (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 576 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 18560 4640 13920
Cusp forms 18304 4576 13728
Eisenstein series 256 64 192

Trace form

\( 4576 q + 16 q^{3} - 8 q^{5} + 8 q^{7} - 16 q^{9} + O(q^{10}) \) \( 4576 q + 16 q^{3} - 8 q^{5} + 8 q^{7} - 16 q^{9} + 8 q^{11} - 8 q^{13} + 16 q^{15} - 32 q^{17} + 32 q^{19} - 16 q^{21} + 8 q^{23} - 8 q^{25} + 16 q^{27} - 8 q^{29} + 32 q^{35} - 32 q^{37} + 16 q^{39} - 8 q^{41} + 8 q^{43} - 16 q^{45} + 8 q^{47} - 8 q^{49} + 16 q^{51} - 32 q^{53} + 32 q^{55} - 16 q^{57} + 8 q^{59} - 8 q^{61} + 32 q^{63} - 16 q^{65} + 8 q^{67} - 16 q^{69} + 32 q^{71} - 32 q^{73} + 16 q^{75} - 8 q^{77} + 8 q^{79} - 16 q^{81} + 8 q^{83} - 8 q^{85} + 16 q^{87} - 32 q^{89} + 32 q^{91} - 232 q^{93} + 16 q^{99} + O(q^{100}) \)

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

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