Properties

Label 684.3.bf
Level $684$
Weight $3$
Character orbit 684.bf
Rep. character $\chi_{684}(335,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $472$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 684 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472q - 6q^{2} - 2q^{4} - 6q^{5} + 15q^{6} + 6q^{9} + O(q^{10}) \) \( 472q - 6q^{2} - 2q^{4} - 6q^{5} + 15q^{6} + 6q^{9} - 6q^{10} + 27q^{12} - 3q^{14} - 2q^{16} - 72q^{17} - 12q^{18} - 69q^{20} - 60q^{21} + 21q^{22} + 59q^{24} + 1102q^{25} - 18q^{28} - 6q^{29} + 25q^{30} - 6q^{32} + 48q^{33} + 15q^{34} + q^{36} - 81q^{38} - 78q^{40} - 186q^{41} + 4q^{42} + 147q^{44} + 42q^{45} + 393q^{48} + 1480q^{49} - 75q^{50} + 168q^{54} - 98q^{57} - 10q^{58} + 297q^{60} + 2q^{61} + 12q^{62} - 272q^{64} - 144q^{65} + 79q^{66} - 54q^{68} - 54q^{69} + 144q^{70} - 237q^{72} - 16q^{73} + 93q^{76} - 12q^{77} + 372q^{78} - 510q^{80} - 122q^{81} - 10q^{82} - 288q^{84} - 204q^{85} + 318q^{86} - 15q^{90} + 34q^{93} + 24q^{94} - 145q^{96} + 336q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

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