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Properties

Label 784.6.bk
Level $784$
Weight $6$
Character orbit 784.bk
Rep. character $\chi_{784}(27,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $6696$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 784.bk (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(784, [\chi])\).

Total New Old
Modular forms 6744 6744 0
Cusp forms 6696 6696 0
Eisenstein series 48 48 0

Trace form

\( 6696 q - 10 q^{2} - 14 q^{3} - 10 q^{4} - 14 q^{5} - 14 q^{6} - 24 q^{7} + 482 q^{8} + O(q^{10}) \) \( 6696 q - 10 q^{2} - 14 q^{3} - 10 q^{4} - 14 q^{5} - 14 q^{6} - 24 q^{7} + 482 q^{8} - 14 q^{10} - 10 q^{11} - 14 q^{12} - 14 q^{13} - 1188 q^{14} - 10 q^{16} - 28 q^{17} - 8172 q^{18} - 14 q^{20} - 498 q^{21} - 10066 q^{22} - 20 q^{23} - 14 q^{24} - 14 q^{26} - 14 q^{27} + 52878 q^{28} - 10 q^{29} - 152 q^{30} - 3830 q^{32} - 28 q^{33} + 86114 q^{34} - 8650 q^{35} - 4106 q^{36} - 10 q^{37} - 14 q^{38} - 20 q^{39} + 210434 q^{40} - 4974 q^{42} - 10 q^{43} - 12286 q^{44} - 14 q^{45} + 50138 q^{46} - 24 q^{49} - 68684 q^{50} + 15378 q^{51} - 14 q^{52} - 10 q^{53} - 14 q^{54} - 28 q^{55} + 461356 q^{56} + 44946 q^{58} - 14 q^{59} - 42606 q^{60} - 14 q^{61} - 462 q^{62} - 49198 q^{64} - 20 q^{65} + 694526 q^{66} - 89280 q^{67} - 14 q^{69} + 140786 q^{70} - 719220 q^{71} - 131082 q^{72} - 24254 q^{74} - 14 q^{75} - 147224 q^{76} + 33602 q^{77} + 347378 q^{78} + 7112104 q^{81} + 880446 q^{82} - 14 q^{83} + 963472 q^{84} - 12510 q^{85} + 361616 q^{86} - 28 q^{87} - 778700 q^{88} - 14 q^{90} + 401990 q^{91} - 311552 q^{92} - 2440 q^{93} - 433622 q^{94} + 2753828 q^{96} + 1013324 q^{98} - 237192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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