Properties

Label 684.3.bh
Level $684$
Weight $3$
Character orbit 684.bh
Rep. character $\chi_{684}(227,\cdot)$
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.bh (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

\( 472 q - 2 q^{4} - 12 q^{5} - 12 q^{6} + O(q^{10}) \) \( 472 q - 2 q^{4} - 12 q^{5} - 12 q^{6} - 2 q^{16} + 120 q^{20} - 46 q^{24} + 1096 q^{25} - 72 q^{28} - 116 q^{30} + 124 q^{36} + 75 q^{38} - 8 q^{42} - 108 q^{45} + 1480 q^{49} - 78 q^{54} - 68 q^{57} + 14 q^{58} - 4 q^{61} - 272 q^{64} + 82 q^{66} + 90 q^{68} - 64 q^{73} - 360 q^{74} + 93 q^{76} - 12 q^{77} - 608 q^{81} + 8 q^{82} + 96 q^{85} - 906 q^{92} + 28 q^{93} + 584 q^{96} + O(q^{100}) \)

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

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