Properties

Label 2304.3.bf
Level $2304$
Weight $3$
Character orbit 2304.bf
Rep. character $\chi_{2304}(271,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $632$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2304.bf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 6272 648 5624
Cusp forms 6016 632 5384
Eisenstein series 256 16 240

Trace form

\( 632q + 8q^{5} + 8q^{7} + O(q^{10}) \) \( 632q + 8q^{5} + 8q^{7} - 8q^{11} - 8q^{13} + 8q^{17} + 8q^{19} - 8q^{23} - 8q^{25} + 8q^{29} + 16q^{31} - 8q^{35} - 8q^{37} + 8q^{41} + 8q^{43} - 8q^{47} - 8q^{49} + 8q^{53} - 504q^{55} + 248q^{59} - 8q^{61} + 16q^{65} - 56q^{67} - 520q^{71} - 8q^{73} + 8q^{77} + 520q^{79} - 8q^{83} - 8q^{85} + 8q^{89} + 8q^{91} - 16q^{95} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)