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

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

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

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