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Properties

Label 288.8.p
Level $288$
Weight $8$
Character orbit 288.p
Rep. character $\chi_{288}(47,\cdot)$
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.p (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

\( 164 q + 4 q^{3} - 4 q^{9} + O(q^{10}) \) \( 164 q + 4 q^{3} - 4 q^{9} + 6 q^{11} + 8 q^{19} - 1156252 q^{25} + 238048 q^{27} - 103394 q^{33} - 901818 q^{41} + 2 q^{43} + 8235428 q^{49} - 1125964 q^{51} + 334420 q^{57} + 11841522 q^{59} - 6 q^{65} + 2 q^{67} - 8 q^{73} - 1628996 q^{75} - 6421744 q^{81} + 14348826 q^{83} + 3294180 q^{91} - 2 q^{97} + 14430806 q^{99} + O(q^{100}) \)

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

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