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Properties

Label 576.8.bm
Level $576$
Weight $8$
Character orbit 576.bm
Rep. character $\chi_{576}(13,\cdot)$
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.bm (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

\( 10720 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} + O(q^{10}) \) \( 10720 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} - 1196096 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} + 1739904 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 4069536 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} - 7717856 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 10358144 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 2080 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 1040 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} - 29207192 q^{76} - 8 q^{77} - 39347608 q^{78} - 8 q^{79} + 93615968 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 17056832 q^{84} - 8 q^{85} - 139071096 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 31734016 q^{90} - 32 q^{91} - 54440784 q^{92} - 17512 q^{93} - 8 q^{94} + 112868968 q^{96} + 125538032 q^{98} - 16 q^{99} + O(q^{100}) \)

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.