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Properties

Label 819.2.fk
Level $819$
Weight $2$
Character orbit 819.fk
Rep. character $\chi_{819}(31,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

Total New Old
Modular forms 464 464 0
Cusp forms 432 432 0
Eisenstein series 32 32 0

Trace form

\( 432 q + 2 q^{2} - 12 q^{3} + 12 q^{6} - 8 q^{8} - 4 q^{9} + O(q^{10}) \) \( 432 q + 2 q^{2} - 12 q^{3} + 12 q^{6} - 8 q^{8} - 4 q^{9} - 12 q^{11} - 4 q^{14} - 14 q^{15} + 196 q^{16} + 14 q^{18} - 12 q^{19} - 60 q^{20} - 8 q^{22} - 24 q^{24} - 12 q^{26} - 36 q^{27} + 4 q^{28} - 24 q^{29} - 30 q^{31} + 10 q^{32} - 60 q^{33} - 12 q^{34} - 60 q^{35} - 2 q^{37} - 22 q^{39} - 100 q^{42} + 32 q^{44} - 6 q^{45} + 4 q^{46} + 30 q^{47} - 12 q^{48} + 22 q^{50} + 8 q^{53} + 30 q^{54} - 44 q^{57} + 12 q^{58} - 6 q^{59} - 64 q^{60} - 12 q^{61} + 14 q^{63} + 16 q^{65} - 12 q^{66} + 16 q^{67} + 32 q^{70} + 48 q^{71} + 34 q^{72} - 12 q^{73} + 104 q^{74} - 48 q^{76} + 2 q^{78} + 28 q^{79} - 6 q^{80} - 44 q^{81} + 84 q^{83} - 38 q^{84} - 6 q^{85} + 84 q^{86} + 24 q^{87} + 18 q^{89} + 52 q^{92} - 108 q^{93} - 12 q^{94} + 42 q^{96} + 6 q^{97} - 112 q^{98} - 50 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
819.2.fk.a 819.fk 819.ek $432$ $6.540$ None \(2\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$