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Properties

Label 576.7.bk
Level $576$
Weight $7$
Character orbit 576.bk
Rep. character $\chi_{576}(43,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $9184$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 576.bk (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 576 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(576, [\chi])\).

Total New Old
Modular forms 9248 9248 0
Cusp forms 9184 9184 0
Eisenstein series 64 64 0

Trace form

\( 9184 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} + O(q^{10}) \) \( 9184 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 321984 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} + 206464 q^{30} - 16 q^{31} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 365216 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} - 347616 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} + 1770112 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} + 992 q^{62} - 32 q^{64} - 16 q^{65} - 528 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} - 3423896 q^{76} - 8 q^{77} + 4734824 q^{78} - 8 q^{79} - 4176032 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 5971520 q^{84} - 8 q^{85} + 1656712 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} + 11465984 q^{90} - 32 q^{91} - 10105424 q^{92} + 5816 q^{93} - 8 q^{94} - 16 q^{95} - 3708056 q^{96} - 20697872 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

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