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Properties

Label 3456.2.bo
Level $3456$
Weight $2$
Character orbit 3456.bo
Rep. character $\chi_{3456}(145,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $368$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3456.bo (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 288 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3456, [\chi])\).

Total New Old
Modular forms 4800 400 4400
Cusp forms 4416 368 4048
Eisenstein series 384 32 352

Trace form

\( 368 q + 4 q^{5} + 4 q^{7} + O(q^{10}) \) \( 368 q + 4 q^{5} + 4 q^{7} - 4 q^{11} - 4 q^{13} + 16 q^{19} - 4 q^{23} - 4 q^{25} + 4 q^{29} + 8 q^{31} - 16 q^{35} - 16 q^{37} + 4 q^{41} + 4 q^{43} + 16 q^{53} + 16 q^{55} - 4 q^{59} - 4 q^{61} + 8 q^{65} + 4 q^{67} - 16 q^{71} - 16 q^{73} + 4 q^{77} + 36 q^{83} + 16 q^{85} + 16 q^{89} + 16 q^{91} - 136 q^{95} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3456, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)