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Properties

Label 684.5.bf
Level $684$
Weight $5$
Character orbit 684.bf
Rep. character $\chi_{684}(335,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $952$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 684 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 968 968 0
Cusp forms 952 952 0
Eisenstein series 16 16 0

Trace form

\( 952 q - 6 q^{2} - 2 q^{4} - 6 q^{5} + 63 q^{6} - 114 q^{9} + O(q^{10}) \) \( 952 q - 6 q^{2} - 2 q^{4} - 6 q^{5} + 63 q^{6} - 114 q^{9} - 6 q^{10} + 243 q^{12} - 3 q^{14} - 2 q^{16} - 144 q^{17} - 48 q^{18} + 1947 q^{20} - 492 q^{21} + 93 q^{22} - 1477 q^{24} + 57502 q^{25} - 258 q^{28} - 6 q^{29} - 923 q^{30} - 6 q^{32} + 480 q^{33} - 1209 q^{34} - 3023 q^{36} + 6075 q^{38} - 1878 q^{40} + 8274 q^{41} - 9632 q^{42} - 7053 q^{44} + 1242 q^{45} - 5943 q^{48} + 155032 q^{49} - 1875 q^{50} - 3384 q^{54} - 2498 q^{57} - 34 q^{58} + 13617 q^{60} + 2 q^{61} + 48 q^{62} + 1840 q^{64} + 13536 q^{65} - 2369 q^{66} - 774 q^{68} - 486 q^{69} + 7200 q^{70} - 6285 q^{72} + 1700 q^{73} + 1581 q^{76} - 12 q^{77} + 4872 q^{78} - 27150 q^{80} - 19442 q^{81} - 34 q^{82} + 25200 q^{84} - 5004 q^{85} - 52818 q^{86} - 51 q^{90} + 322 q^{93} + 96 q^{94} + 55799 q^{96} + 7104 q^{98} + O(q^{100}) \)

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.