Properties

Label 784.4.bu
Level $784$
Weight $4$
Character orbit 784.bu
Rep. character $\chi_{784}(3,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $8016$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.bu (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(784, [\chi])\).

Total New Old
Modular forms 8112 8112 0
Cusp forms 8016 8016 0
Eisenstein series 96 96 0

Trace form

\( 8016q - 26q^{2} - 22q^{3} - 26q^{4} - 22q^{5} - 28q^{6} - 48q^{7} + 64q^{8} + O(q^{10}) \) \( 8016q - 26q^{2} - 22q^{3} - 26q^{4} - 22q^{5} - 28q^{6} - 48q^{7} + 64q^{8} - 40q^{10} - 26q^{11} - 22q^{12} - 28q^{13} + 168q^{14} - 26q^{16} - 44q^{17} + 90q^{18} - 36q^{19} - 28q^{20} + 30q^{21} - 524q^{22} - 52q^{23} - 22q^{24} - 22q^{26} - 28q^{27} - 178q^{28} - 20q^{29} - 28q^{30} + 464q^{32} - 44q^{33} - 1036q^{34} + 454q^{35} + 236q^{36} - 26q^{37} - 22q^{38} - 52q^{39} - 1354q^{40} - 678q^{42} - 20q^{43} - 4184q^{44} - 184q^{45} - 408q^{46} - 48q^{49} + 1412q^{50} - 618q^{51} - 184q^{52} - 26q^{53} + 5726q^{54} - 56q^{55} + 5888q^{56} - 348q^{58} + 2042q^{59} + 7686q^{60} - 22q^{61} + 84q^{62} - 4976q^{64} - 52q^{65} + 8482q^{66} + 912q^{67} - 3066q^{68} - 28q^{69} - 5760q^{70} + 1080q^{71} - 1050q^{72} + 1052q^{74} - 772q^{75} - 10738q^{76} - 710q^{77} + 9328q^{78} + 22536q^{80} - 51568q^{81} + 6986q^{82} - 28q^{83} - 24784q^{84} + 480q^{85} + 2788q^{86} - 44q^{87} - 2028q^{88} - 28q^{90} + 8556q^{91} - 4924q^{92} + 244q^{93} + 14558q^{94} - 39656q^{96} - 11354q^{98} + 2976q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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