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Properties

Label 693.2.bn
Level $693$
Weight $2$
Character orbit 693.bn
Rep. character $\chi_{693}(263,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $184$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(693, [\chi])\).

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184 q - 2 q^{3} + 172 q^{4} - 6 q^{5} - 6 q^{9} + O(q^{10}) \) \( 184 q - 2 q^{3} + 172 q^{4} - 6 q^{5} - 6 q^{9} + 3 q^{11} - 30 q^{12} - 6 q^{14} - 6 q^{15} + 148 q^{16} - 24 q^{20} - 6 q^{22} + 12 q^{23} + 78 q^{25} - 36 q^{26} - 14 q^{27} - 4 q^{31} + 5 q^{33} - 56 q^{36} - 4 q^{37} - 54 q^{42} - 39 q^{44} - 46 q^{45} - 98 q^{48} - 2 q^{49} - 24 q^{53} - 10 q^{55} - 60 q^{56} + 6 q^{58} - 6 q^{60} + 88 q^{64} - 60 q^{66} - 4 q^{67} - 10 q^{69} - 42 q^{70} + 16 q^{75} - 58 q^{78} - 108 q^{80} + 26 q^{81} + 18 q^{86} - 3 q^{88} - 30 q^{89} - 36 q^{91} + 78 q^{92} + 12 q^{93} - 4 q^{97} + 70 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
693.2.bn.a 693.bn 693.an $184$ $5.534$ None \(0\) \(-2\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$