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Properties

Label 819.2.bt
Level $819$
Weight $2$
Character orbit 819.bt
Rep. character $\chi_{819}(311,\cdot)$
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.bt (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

\( 216 q - 6 q^{3} - 102 q^{4} - 6 q^{9} + O(q^{10}) \) \( 216 q - 6 q^{3} - 102 q^{4} - 6 q^{9} - 12 q^{10} - 6 q^{12} - 3 q^{13} - 6 q^{14} - 90 q^{16} - 12 q^{22} - 188 q^{25} - 6 q^{26} + 18 q^{27} - 12 q^{29} + 14 q^{30} + 60 q^{35} - 16 q^{36} - 72 q^{38} - 24 q^{39} + 6 q^{42} + 4 q^{43} + 54 q^{48} + 40 q^{51} - 24 q^{53} - 48 q^{56} - 48 q^{61} - 12 q^{62} + 120 q^{64} - 54 q^{65} + 6 q^{66} - 12 q^{68} - 24 q^{69} - 6 q^{75} + 66 q^{77} + q^{78} + 16 q^{79} - 30 q^{81} - 24 q^{82} - 24 q^{87} + 12 q^{88} - 48 q^{90} - q^{91} + 78 q^{92} - 6 q^{94} + 54 q^{95} + O(q^{100}) \)

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