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Properties

Label 288.8.s
Level $288$
Weight $8$
Character orbit 288.s
Rep. character $\chi_{288}(95,\cdot)$
Character field $\Q(\zeta_{6})$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 168 q - 2236 q^{9} + O(q^{10}) \) \( 168 q - 2236 q^{9} - 2344 q^{21} + 1312500 q^{25} + 384072 q^{29} + 166900 q^{33} - 2705436 q^{41} - 912536 q^{45} + 9882516 q^{49} + 1084068 q^{57} - 12644688 q^{65} + 12533072 q^{69} - 6405528 q^{73} - 17847696 q^{77} - 10358732 q^{81} + 34657088 q^{93} + 10592724 q^{97} + O(q^{100}) \)

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

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