Properties

Label 819.2.bn
Level $819$
Weight $2$
Character orbit 819.bn
Rep. character $\chi_{819}(185,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
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.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
Character field: \(\Q(\zeta_{6})\)
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 232 232 0
Cusp forms 216 216 0
Eisenstein series 16 16 0

Trace form

\( 216 q - 206 q^{4} - 12 q^{5} + 12 q^{6} + 2 q^{7} + 2 q^{9} + O(q^{10}) \) \( 216 q - 206 q^{4} - 12 q^{5} + 12 q^{6} + 2 q^{7} + 2 q^{9} + 9 q^{11} - 6 q^{12} + 3 q^{13} - 6 q^{14} - 3 q^{15} + 190 q^{16} + 14 q^{18} + 24 q^{20} - 2 q^{21} + 10 q^{22} + 15 q^{23} - 24 q^{24} + 180 q^{25} + 24 q^{26} + 18 q^{27} - 22 q^{28} - 6 q^{29} + 23 q^{30} + 6 q^{31} + 42 q^{33} + 6 q^{34} + 3 q^{35} - 12 q^{36} + q^{37} + 48 q^{38} - 9 q^{39} + 21 q^{42} + 4 q^{43} - 66 q^{44} - 3 q^{45} + 10 q^{46} - 24 q^{47} - 6 q^{48} - 6 q^{49} + 2 q^{51} - 36 q^{52} + 12 q^{53} - 15 q^{54} - 15 q^{55} + 12 q^{56} + 10 q^{57} + 7 q^{58} - 6 q^{59} - 41 q^{60} + 18 q^{61} - 24 q^{62} + 7 q^{63} - 172 q^{64} + 24 q^{65} + 6 q^{67} - 3 q^{68} - 57 q^{69} - 45 q^{70} - 82 q^{72} - 12 q^{73} + 87 q^{74} + 51 q^{75} - 42 q^{77} + 4 q^{78} - 3 q^{79} - 162 q^{80} - 26 q^{81} + 9 q^{84} - 9 q^{85} - 27 q^{87} - 13 q^{88} + 15 q^{89} - 96 q^{90} - 15 q^{91} - 24 q^{92} + 37 q^{93} - 3 q^{94} + 42 q^{96} + 60 q^{98} - 29 q^{99} + O(q^{100}) \)

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.bn.a 819.bn 819.an $216$ $6.540$ None \(0\) \(0\) \(-12\) \(2\) $\mathrm{SU}(2)[C_{6}]$