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Properties

Label 684.5.cb
Level $684$
Weight $5$
Character orbit 684.cb
Rep. character $\chi_{684}(283,\cdot)$
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.cb (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

\( 2856 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{8} + 324 q^{9} + O(q^{10}) \) \( 2856 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{8} + 324 q^{9} - 12 q^{10} - 3 q^{12} - 6 q^{13} - 99 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{18} - 6 q^{20} - 498 q^{21} + 189 q^{22} - 2664 q^{24} - 6 q^{25} + 3090 q^{26} + 756 q^{28} - 6 q^{29} + 963 q^{30} - 3 q^{32} - 3120 q^{33} - 2415 q^{34} + 4254 q^{36} - 48 q^{37} - 3 q^{38} + 3747 q^{40} + 16554 q^{41} + 7695 q^{42} - 7065 q^{44} - 6 q^{45} - 6 q^{46} - 17496 q^{48} + 465114 q^{49} - 6 q^{50} - 3 q^{52} - 24 q^{53} - 13539 q^{54} - 7209 q^{56} - 12 q^{57} - 6 q^{58} - 30753 q^{60} - 6 q^{61} + 36 q^{62} - 1392 q^{64} - 12 q^{65} + 15030 q^{66} + 3 q^{68} - 6 q^{69} - 14409 q^{70} + 6276 q^{72} - 10248 q^{73} + 65973 q^{74} - 3 q^{76} + 28800 q^{77} + 9843 q^{78} - 12 q^{80} + 28548 q^{81} - 12 q^{82} - 14409 q^{84} - 6 q^{85} + 26403 q^{86} + 24579 q^{88} - 24 q^{89} + 43767 q^{90} - 77871 q^{92} + 960 q^{93} - 6 q^{94} + 49305 q^{96} - 33846 q^{97} + 35853 q^{98} + O(q^{100}) \)

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.