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Properties

Label 288.8.r
Level $288$
Weight $8$
Character orbit 288.r
Rep. character $\chi_{288}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $164$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 288.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
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 688 172 516
Cusp forms 656 164 492
Eisenstein series 32 8 24

Trace form

\( 164 q + 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 164 q + 2 q^{7} - 4 q^{9} + 4378 q^{15} - 8 q^{17} - 146002 q^{23} + 1156248 q^{25} + 2 q^{31} + 94638 q^{33} + 146350 q^{39} + 300602 q^{41} + 2076462 q^{47} - 8235432 q^{49} + 312508 q^{55} + 351916 q^{57} - 11485202 q^{63} - 312502 q^{65} + 20043024 q^{71} - 8 q^{73} + 2 q^{79} - 335456 q^{81} - 2067066 q^{87} + 7614440 q^{89} + 27279752 q^{95} - 2 q^{97} + O(q^{100}) \)

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

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