Properties

Label 819.2.dr
Level $819$
Weight $2$
Character orbit 819.dr
Rep. character $\chi_{819}(88,\cdot)$
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.dr (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

\( 216 q - 3 q^{2} - 2 q^{3} + 103 q^{4} - 6 q^{6} - 3 q^{7} - 6 q^{9} + O(q^{10}) \) \( 216 q - 3 q^{2} - 2 q^{3} + 103 q^{4} - 6 q^{6} - 3 q^{7} - 6 q^{9} + 4 q^{10} + 3 q^{11} + 8 q^{12} - q^{13} - 10 q^{14} - 12 q^{15} - 95 q^{16} + 18 q^{17} - 12 q^{18} + 18 q^{20} + 9 q^{21} - 20 q^{22} + 10 q^{23} - 12 q^{24} + 94 q^{25} - 2 q^{26} - 14 q^{27} - 6 q^{28} + 4 q^{29} - 43 q^{30} + 9 q^{32} + 12 q^{33} - 6 q^{34} - 23 q^{35} + 14 q^{36} - 3 q^{37} + 12 q^{38} - 10 q^{39} - 4 q^{40} - 6 q^{41} + 6 q^{43} - 18 q^{44} - 33 q^{45} - 6 q^{46} + 38 q^{48} + 3 q^{49} - 45 q^{50} - 32 q^{51} - 7 q^{52} - 18 q^{53} + 15 q^{54} + q^{55} + 18 q^{56} - 36 q^{57} + 3 q^{58} - 3 q^{59} - 54 q^{60} - 8 q^{61} + 24 q^{62} - 172 q^{64} - q^{65} - 21 q^{66} - 24 q^{67} + 138 q^{68} - 34 q^{69} - 6 q^{70} - 60 q^{71} - 12 q^{72} - 42 q^{73} - 54 q^{74} - 16 q^{75} + 6 q^{76} + 32 q^{77} - 16 q^{78} - 14 q^{79} - 42 q^{81} + 4 q^{82} - 42 q^{83} + 6 q^{84} + 90 q^{86} + 7 q^{87} - 13 q^{88} - 21 q^{89} - 68 q^{90} + 21 q^{91} + 56 q^{92} + 15 q^{93} + 7 q^{94} - 3 q^{95} - 12 q^{96} - 9 q^{97} - 120 q^{98} - 51 q^{99} + O(q^{100}) \)

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.dr.a 819.dr 819.cr $2$ $6.540$ \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
819.2.dr.b 819.dr 819.cr $214$ $6.540$ None \(0\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$