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Properties

Label 760.2.cj
Level $760$
Weight $2$
Character orbit 760.cj
Rep. character $\chi_{760}(149,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 760.cj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(760, [\chi])\).

Total New Old
Modular forms 744 744 0
Cusp forms 696 696 0
Eisenstein series 48 48 0

Trace form

\( 696 q - 6 q^{4} - 18 q^{6} - 24 q^{9} + O(q^{10}) \) \( 696 q - 6 q^{4} - 18 q^{6} - 24 q^{9} - 15 q^{10} - 42 q^{14} - 12 q^{15} - 6 q^{16} - 42 q^{20} - 36 q^{24} - 12 q^{25} + 18 q^{26} + 18 q^{30} - 84 q^{31} + 12 q^{34} + 30 q^{36} - 48 q^{39} - 18 q^{40} - 24 q^{41} - 36 q^{44} - 6 q^{46} + 264 q^{49} + 6 q^{50} - 60 q^{54} - 42 q^{55} - 108 q^{56} - 30 q^{60} - 30 q^{64} - 6 q^{65} - 48 q^{66} - 63 q^{70} - 24 q^{71} - 126 q^{74} - 48 q^{76} - 24 q^{79} + 45 q^{80} + 12 q^{81} - 126 q^{84} - 6 q^{86} - 24 q^{89} - 66 q^{90} + 36 q^{94} + 48 q^{95} - 72 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(760, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
760.2.cj.a 760.cj 760.bj $696$ $6.069$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$