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Properties

Label 819.2.be
Level $819$
Weight $2$
Character orbit 819.be
Rep. character $\chi_{819}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 232 192 40
Cusp forms 216 192 24
Eisenstein series 16 0 16

Trace form

\( 192 q - 192 q^{4} + 8 q^{9} + O(q^{10}) \) \( 192 q - 192 q^{4} + 8 q^{9} + 30 q^{12} - 42 q^{14} - 6 q^{15} + 192 q^{16} - 18 q^{17} - 10 q^{18} + 4 q^{21} - 18 q^{23} - 96 q^{25} + 36 q^{27} + 36 q^{29} - 22 q^{30} - 24 q^{36} - 30 q^{38} - 12 q^{41} + 30 q^{42} + 66 q^{44} - 84 q^{45} + 12 q^{46} - 60 q^{48} - 12 q^{49} - 48 q^{50} - 10 q^{51} - 24 q^{53} - 84 q^{54} + 96 q^{56} + 10 q^{57} + 12 q^{58} + 60 q^{59} + 100 q^{60} + 36 q^{62} + 4 q^{63} - 192 q^{64} + 30 q^{66} + 42 q^{68} - 36 q^{70} + 2 q^{72} - 48 q^{75} - 6 q^{77} + 10 q^{78} + 24 q^{79} - 80 q^{81} - 60 q^{83} - 102 q^{84} - 60 q^{86} - 48 q^{87} + 84 q^{89} + 54 q^{90} + 42 q^{92} - 38 q^{93} - 84 q^{96} + 102 q^{98} + 10 q^{99} + O(q^{100}) \)

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.be.a 819.be 63.i $192$ $6.540$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)