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Properties

Label 576.8.bb
Level $576$
Weight $8$
Character orbit 576.bb
Rep. character $\chi_{576}(49,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $664$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(576, [\chi])\).

Total New Old
Modular forms 2720 680 2040
Cusp forms 2656 664 1992
Eisenstein series 64 16 48

Trace form

\( 664 q + 4 q^{3} - 2 q^{5} + O(q^{10}) \) \( 664 q + 4 q^{3} - 2 q^{5} + 2 q^{11} - 2 q^{13} + 8 q^{15} - 16 q^{17} + 8 q^{19} - 4378 q^{21} - 238040 q^{27} - 2 q^{29} + 4 q^{31} - 8 q^{33} + 312508 q^{35} - 8 q^{37} + 2 q^{43} - 156254 q^{45} - 4152916 q^{47} + 36235888 q^{49} + 1125972 q^{51} - 8 q^{53} + 3947174 q^{59} - 2 q^{61} + 3294180 q^{63} - 4 q^{65} + 2 q^{67} - 4378 q^{69} - 1620248 q^{75} - 3294174 q^{77} + 4 q^{79} - 8 q^{81} - 4782938 q^{83} - 156252 q^{85} + 3294180 q^{91} + 14504138 q^{93} + 54872004 q^{95} - 4 q^{97} + 14430806 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)