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Properties

Label 576.8.i
Level $576$
Weight $8$
Character orbit 576.i
Rep. character $\chi_{576}(193,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $332$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 576.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1368 340 1028
Cusp forms 1320 332 988
Eisenstein series 48 8 40

Trace form

\( 332 q + 2 q^{5} - 4 q^{9} + O(q^{10}) \) \( 332 q + 2 q^{5} - 4 q^{9} + 2 q^{13} - 8 q^{17} - 4370 q^{21} - 2468752 q^{25} + 2 q^{29} - 193662 q^{33} + 8 q^{37} + 601206 q^{41} - 1261710 q^{45} - 18117948 q^{49} + 7731992 q^{53} + 677592 q^{57} + 2 q^{61} + 312498 q^{65} + 1869814 q^{69} - 8 q^{73} - 3294170 q^{77} + 12843476 q^{81} + 156252 q^{85} - 15228904 q^{89} + 60913174 q^{93} - 2 q^{97} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)