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

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

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

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