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Properties

Label 684.2.ch
Level $684$
Weight $2$
Character orbit 684.ch
Rep. character $\chi_{684}(47,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 684.ch (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 684 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(684, [\chi])\).

Total New Old
Modular forms 744 744 0
Cusp forms 696 696 0
Eisenstein series 48 48 0

Trace form

\( 696 q - 9 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{6} + O(q^{10}) \) \( 696 q - 9 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{6} - 12 q^{10} - 3 q^{12} - 6 q^{13} - 9 q^{14} - 3 q^{16} - 12 q^{18} - 18 q^{20} - 30 q^{21} - 27 q^{22} - 18 q^{24} - 6 q^{25} - 72 q^{26} - 18 q^{29} + 63 q^{30} - 9 q^{32} - 60 q^{33} - 39 q^{34} - 66 q^{36} - 48 q^{37} - 9 q^{38} - 33 q^{40} - 18 q^{41} - 27 q^{42} - 135 q^{44} - 6 q^{45} - 6 q^{46} - 18 q^{48} + 282 q^{49} - 3 q^{52} + 15 q^{54} + 45 q^{56} - 12 q^{57} - 6 q^{58} - 9 q^{60} - 6 q^{61} + 18 q^{62} + 12 q^{64} + 18 q^{66} - 9 q^{68} - 6 q^{69} - 45 q^{70} + 12 q^{72} + 12 q^{73} + 99 q^{74} - 3 q^{76} - 36 q^{77} + 69 q^{78} - 72 q^{81} - 12 q^{82} - 45 q^{84} - 6 q^{85} - 171 q^{86} - 45 q^{88} + 27 q^{90} - 9 q^{92} + 24 q^{93} - 6 q^{94} - 87 q^{96} - 42 q^{97} - 45 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
684.2.ch.a 684.ch 684.bh $696$ $5.462$ None \(-9\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{18}]$