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Properties

Label 819.2.ch
Level $819$
Weight $2$
Character orbit 819.ch
Rep. character $\chi_{819}(524,\cdot)$
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.ch (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

\( 216 q - 6 q^{2} - 102 q^{4} + 24 q^{8} + O(q^{10}) \) \( 216 q - 6 q^{2} - 102 q^{4} + 24 q^{8} - 6 q^{11} - 6 q^{14} - 24 q^{15} - 90 q^{16} - 24 q^{18} - 9 q^{21} + 18 q^{22} + 88 q^{25} - 12 q^{28} - 6 q^{29} - 10 q^{30} - 30 q^{32} + 18 q^{35} + 26 q^{36} - 18 q^{37} + 12 q^{39} - 42 q^{42} - 20 q^{43} + 72 q^{44} - 12 q^{46} - 6 q^{49} - 96 q^{50} - 20 q^{51} - 36 q^{57} - 6 q^{58} + 78 q^{60} - 24 q^{63} + 120 q^{64} - 42 q^{65} - 15 q^{70} - 24 q^{71} - 18 q^{72} - 18 q^{77} - 38 q^{78} - 8 q^{79} - 24 q^{81} - 78 q^{84} + 42 q^{85} - 84 q^{86} + 54 q^{88} - 22 q^{91} - 120 q^{92} + 12 q^{93} - 36 q^{95} + 78 q^{99} + O(q^{100}) \)

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