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Properties

Label 576.8.bd
Level $576$
Weight $8$
Character orbit 576.bd
Rep. character $\chi_{576}(37,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2232$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 5408 2248 3160
Cusp forms 5344 2232 3112
Eisenstein series 64 16 48

Trace form

\( 2232 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} + O(q^{10}) \) \( 2232 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 274448 q^{22} + 8 q^{23} - 8 q^{25} + 727968 q^{26} + 390912 q^{28} + 8 q^{29} - 1071312 q^{32} + 403152 q^{34} + 8 q^{35} - 8 q^{37} + 1244928 q^{38} - 2686368 q^{40} + 8 q^{41} - 8 q^{43} + 3370480 q^{44} - 8 q^{46} + 8 q^{47} - 8 q^{49} - 2317408 q^{50} - 10204952 q^{52} + 8 q^{53} - 8382024 q^{55} - 10737264 q^{56} - 10358144 q^{58} + 3671880 q^{59} - 8 q^{61} + 10346488 q^{62} - 22837160 q^{64} + 16 q^{65} + 776264 q^{67} - 8750056 q^{68} + 35990296 q^{70} + 24697416 q^{71} - 8 q^{73} + 4214400 q^{74} + 19471448 q^{76} + 8 q^{77} + 523736 q^{79} + 15253552 q^{80} + 49314632 q^{82} + 8 q^{83} - 8 q^{85} - 69535536 q^{86} - 52517848 q^{88} + 8 q^{89} - 8 q^{91} + 54440784 q^{92} + 74691544 q^{94} + 62769040 q^{98} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)