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Properties

Label 819.2.cv
Level $819$
Weight $2$
Character orbit 819.cv
Rep. character $\chi_{819}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.cv (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 232 232 0
Cusp forms 216 216 0
Eisenstein series 16 16 0

Trace form

\( 216 q + 3 q^{2} + q^{3} + 103 q^{4} - 6 q^{6} - 3 q^{7} + 3 q^{9} + O(q^{10}) \) \( 216 q + 3 q^{2} + q^{3} + 103 q^{4} - 6 q^{6} - 3 q^{7} + 3 q^{9} - 2 q^{10} - 3 q^{11} - 4 q^{12} - q^{13} + 2 q^{14} - 12 q^{15} - 95 q^{16} - 36 q^{17} + 18 q^{20} - 20 q^{22} - 5 q^{23} + 6 q^{24} - 188 q^{25} + 4 q^{26} - 14 q^{27} - 12 q^{28} + 4 q^{29} + 29 q^{30} - 12 q^{31} - 9 q^{32} - 3 q^{33} - 6 q^{34} + 7 q^{35} + 14 q^{36} - 24 q^{38} + 17 q^{39} + 8 q^{40} - 6 q^{41} - 54 q^{42} + 6 q^{43} + 18 q^{44} + 60 q^{45} + 18 q^{47} + 38 q^{48} + 3 q^{49} - 45 q^{50} - 2 q^{51} - 10 q^{52} - 18 q^{53} + 6 q^{54} + q^{55} - 6 q^{56} - 36 q^{57} - 3 q^{58} + 3 q^{59} - 3 q^{60} + 16 q^{61} + 24 q^{62} - 9 q^{63} - 172 q^{64} + 5 q^{65} - 6 q^{66} - 69 q^{68} - 34 q^{69} + 21 q^{70} - 60 q^{71} + 57 q^{72} + 42 q^{73} + 27 q^{74} + 53 q^{75} + 6 q^{76} - 34 q^{77} - 16 q^{78} + 7 q^{79} + 117 q^{80} + 3 q^{81} - 2 q^{82} - 42 q^{83} + 36 q^{84} - 20 q^{87} - 13 q^{88} - 68 q^{90} - 12 q^{91} + 56 q^{92} + 42 q^{93} - 14 q^{94} - 3 q^{95} + 6 q^{96} - 9 q^{97} + 18 q^{98} - 51 q^{99} + O(q^{100}) \)

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.cv.a 819.cv 819.bv $2$ $6.540$ \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
819.2.cv.b 819.cv 819.bv $214$ $6.540$ None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$