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Properties

Label 576.8.bl
Level $576$
Weight $8$
Character orbit 576.bl
Rep. character $\chi_{576}(11,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $10720$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 576.bl (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 576 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 10784 10784 0
Cusp forms 10720 10720 0
Eisenstein series 64 64 0

Trace form

\( 10720 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} + O(q^{10}) \) \( 10720 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} - 16 q^{12} - 8 q^{13} - 24 q^{14} - 16 q^{15} - 8 q^{16} - 16 q^{18} - 32 q^{19} - 24 q^{20} - 16 q^{21} - 8 q^{22} - 24 q^{23} + 1196064 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 1739936 q^{30} - 16 q^{31} - 24 q^{32} - 8 q^{34} + 4069504 q^{36} - 32 q^{37} - 24 q^{38} - 16 q^{39} - 8 q^{40} - 24 q^{41} + 7717824 q^{42} - 8 q^{43} - 16 q^{45} - 32 q^{46} - 24 q^{47} - 16 q^{48} - 8 q^{49} - 24 q^{50} - 16 q^{51} - 8 q^{52} - 16 q^{54} - 32 q^{55} - 24 q^{56} - 16 q^{57} + 10358128 q^{58} - 24 q^{59} - 16 q^{60} - 8 q^{61} - 32 q^{64} - 48 q^{65} + 1008 q^{66} - 8 q^{67} - 24 q^{68} - 16 q^{69} - 8 q^{70} - 16 q^{72} - 32 q^{73} - 24 q^{74} - 16 q^{75} + 29207176 q^{76} - 24 q^{77} - 39347608 q^{78} - 8 q^{79} - 16 q^{81} - 32 q^{82} - 24 q^{83} - 17056832 q^{84} - 8 q^{85} - 24 q^{86} - 16 q^{87} - 8 q^{88} - 31734016 q^{90} - 32 q^{91} + 163322304 q^{92} + 17480 q^{93} - 8 q^{94} - 48 q^{95} + 112868968 q^{96} - 16 q^{99} + O(q^{100}) \)

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.