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Properties

Label 784.6.bh
Level $784$
Weight $6$
Character orbit 784.bh
Rep. character $\chi_{784}(29,\cdot)$
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.bh (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

\( 6696 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 10 q^{6} - 502 q^{8} + O(q^{10}) \) \( 6696 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 10 q^{6} - 502 q^{8} + 1058 q^{10} - 10 q^{11} - 10 q^{12} - 10 q^{13} + 1164 q^{14} - 20 q^{15} - 10 q^{16} - 20 q^{17} + 7868 q^{18} - 24 q^{19} - 7610 q^{20} - 498 q^{21} - 10066 q^{22} - 11030 q^{24} - 10 q^{26} - 982 q^{27} - 50722 q^{28} - 10 q^{29} + 104 q^{30} - 138432 q^{31} + 3810 q^{32} - 20 q^{33} - 61402 q^{34} - 8650 q^{35} - 4106 q^{36} - 10 q^{37} - 34830 q^{38} + 91070 q^{40} - 33414 q^{42} - 10 q^{43} + 60666 q^{44} - 11538 q^{45} + 49882 q^{46} - 88380 q^{47} + 183584 q^{48} - 24 q^{49} + 68380 q^{50} - 15398 q^{51} - 86470 q^{52} - 10 q^{53} - 300718 q^{54} + 394128 q^{56} - 150190 q^{58} + 28950 q^{59} - 34414 q^{60} - 10 q^{61} + 308038 q^{62} - 67252 q^{63} + 325682 q^{64} - 20 q^{65} - 368542 q^{66} + 89232 q^{67} + 29892 q^{68} - 982 q^{69} - 340438 q^{70} - 131082 q^{72} + 24234 q^{74} + 11518 q^{75} + 105140 q^{76} - 33626 q^{77} + 541954 q^{78} - 48 q^{79} - 1350220 q^{80} + 7112104 q^{81} + 628762 q^{82} - 329250 q^{83} - 1264436 q^{84} + 12490 q^{85} - 361636 q^{86} + 778680 q^{88} - 62902 q^{90} - 469242 q^{91} - 381036 q^{92} - 2440 q^{93} - 48986 q^{94} - 76868 q^{95} - 2165400 q^{96} - 48 q^{97} - 940976 q^{98} - 235248 q^{99} + O(q^{100}) \)

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.