Properties

Label 2304.2.bq
Level $2304$
Weight $2$
Character orbit 2304.bq
Rep. character $\chi_{2304}(49,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $1504$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.bq (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 576 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 6272 1568 4704
Cusp forms 6016 1504 4512
Eisenstein series 256 64 192

Trace form

\( 1504q + 16q^{3} - 8q^{5} + 8q^{7} - 16q^{9} + O(q^{10}) \) \( 1504q + 16q^{3} - 8q^{5} + 8q^{7} - 16q^{9} + 8q^{11} - 8q^{13} + 16q^{15} - 32q^{17} + 32q^{19} - 16q^{21} + 8q^{23} - 8q^{25} + 16q^{27} - 8q^{29} + 32q^{35} - 32q^{37} + 16q^{39} - 8q^{41} + 8q^{43} - 16q^{45} + 8q^{47} - 8q^{49} + 16q^{51} - 32q^{53} + 32q^{55} - 16q^{57} + 8q^{59} - 8q^{61} + 32q^{63} - 16q^{65} + 8q^{67} - 16q^{69} + 32q^{71} - 32q^{73} + 16q^{75} - 8q^{77} + 8q^{79} - 16q^{81} + 8q^{83} - 8q^{85} + 16q^{87} - 32q^{89} + 32q^{91} - 40q^{93} + 16q^{99} + O(q^{100}) \)

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

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