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Properties

Label 288.8.i
Level $288$
Weight $8$
Character orbit 288.i
Rep. character $\chi_{288}(97,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $168$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 288.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(288, [\chi])\).

Total New Old
Modular forms 688 168 520
Cusp forms 656 168 488
Eisenstein series 32 0 32

Trace form

\( 168 q + 2236 q^{9} + O(q^{10}) \) \( 168 q + 2236 q^{9} - 47944 q^{17} - 2344 q^{21} - 1312500 q^{25} - 128024 q^{29} - 427196 q^{33} + 901812 q^{41} + 3123464 q^{45} - 9882516 q^{49} - 7731984 q^{53} - 2490748 q^{57} - 4214896 q^{65} + 1527792 q^{69} - 6405528 q^{73} - 5949232 q^{77} + 7900132 q^{81} - 54705088 q^{89} - 34657088 q^{93} - 10592724 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)