Properties

Label 760.2.z
Level $760$
Weight $2$
Character orbit 760.z
Rep. character $\chi_{760}(349,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $232$
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.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{6})\)
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 248 248 0
Cusp forms 232 232 0
Eisenstein series 16 16 0

Trace form

\( 232q - 4q^{4} + 8q^{6} - 112q^{9} + O(q^{10}) \) \( 232q - 4q^{4} + 8q^{6} - 112q^{9} + 6q^{10} + 8q^{14} + 10q^{15} - 4q^{16} - 6q^{24} - 2q^{25} - 36q^{26} + 16q^{30} + 16q^{31} - 22q^{34} - 8q^{36} + 8q^{39} - 18q^{40} - 4q^{41} + 42q^{44} - 4q^{46} - 200q^{49} + 28q^{50} + 28q^{54} + 8q^{55} + 48q^{56} - 18q^{60} - 100q^{64} + 12q^{65} + 46q^{66} + 42q^{70} + 52q^{71} + 6q^{76} + 20q^{79} - 34q^{80} - 100q^{81} + 32q^{84} + 20q^{86} - 4q^{89} + 48q^{90} - 116q^{94} - 42q^{95} - 20q^{96} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
760.2.z.a \(232\) \(6.069\) None \(0\) \(0\) \(0\) \(0\)