↑

Properties

Label 684.2.u
Level $684$
Weight $2$
Character orbit 684.u
Rep. character $\chi_{684}(103,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $232$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 684.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 684 \)
Character field: \(\Q(\zeta_{6})\)
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 248 248 0
Cusp forms 232 232 0
Eisenstein series 16 16 0

Trace form

\( 232 q - 2 q^{4} + 2 q^{5} - 9 q^{6} - 6 q^{9} + O(q^{10}) \) \( 232 q - 2 q^{4} + 2 q^{5} - 9 q^{6} - 6 q^{9} - 6 q^{10} + 9 q^{12} - 15 q^{14} - 2 q^{16} - 8 q^{17} + 6 q^{18} - 17 q^{20} - 24 q^{21} - 15 q^{22} + 5 q^{24} - 98 q^{25} + 12 q^{26} - 6 q^{28} - 6 q^{29} - 35 q^{30} - 24 q^{33} - 21 q^{34} + q^{36} + 35 q^{38} + 12 q^{40} - 36 q^{41} - 8 q^{42} - 11 q^{44} - 18 q^{45} - 57 q^{48} + 88 q^{49} + 27 q^{50} - 12 q^{53} - 60 q^{56} - 14 q^{57} + 2 q^{58} + 9 q^{60} + 2 q^{61} + 44 q^{62} - 32 q^{64} + 36 q^{65} - 17 q^{66} + 2 q^{68} + 18 q^{69} + 18 q^{70} - 21 q^{72} - 10 q^{73} + 44 q^{74} - 3 q^{76} - 60 q^{77} + 30 q^{78} - 4 q^{80} + 34 q^{81} + 2 q^{82} + 36 q^{85} - 12 q^{89} + 3 q^{90} + 46 q^{92} + 10 q^{93} - 12 q^{94} - 85 q^{96} - 54 q^{98} + O(q^{100}) \)

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.u.a 684.u 684.u $232$ $5.462$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$