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Properties

Label 684.5.br
Level $684$
Weight $5$
Character orbit 684.br
Rep. character $\chi_{684}(155,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2856$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 684.br (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 684 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(684, [\chi])\).

Total New Old
Modular forms 2904 2904 0
Cusp forms 2856 2856 0
Eisenstein series 48 48 0

Trace form

\( 2856 q - 9 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{6} - 180 q^{9} + O(q^{10}) \) \( 2856 q - 9 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{6} - 180 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 3 q^{16} - 18 q^{20} + 960 q^{21} + 93 q^{22} - 5079 q^{24} - 6 q^{25} - 9288 q^{26} + 756 q^{28} - 18 q^{29} + 2580 q^{30} - 9 q^{32} - 1566 q^{33} - 1209 q^{34} - 4266 q^{36} - 9 q^{38} - 1878 q^{40} - 24858 q^{41} - 6558 q^{42} + 25767 q^{44} - 6 q^{45} - 18 q^{46} + 17484 q^{48} - 930228 q^{49} - 9 q^{50} - 3 q^{52} - 27312 q^{54} + 21609 q^{56} - 12 q^{57} - 6 q^{58} + 15489 q^{60} - 6 q^{61} + 144 q^{62} + 1380 q^{64} - 18 q^{65} + 7512 q^{66} - 18 q^{69} + 7200 q^{70} + 6276 q^{72} + 10200 q^{73} + 72900 q^{74} - 3 q^{76} - 36 q^{77} + 5355 q^{78} - 14292 q^{81} - 12 q^{82} - 9 q^{84} - 6 q^{85} - 9 q^{86} - 81735 q^{90} - 9 q^{92} + 474 q^{93} + 29823 q^{96} - 16926 q^{97} + 21465 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

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