Properties

Label 760.2.bp
Level $760$
Weight $2$
Character orbit 760.bp
Rep. character $\chi_{760}(293,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $464$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{12})\)
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 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464q - 6q^{2} - 16q^{7} + O(q^{10}) \) \( 464q - 6q^{2} - 16q^{7} - 6q^{10} - 12q^{15} - 4q^{17} - 32q^{20} + 6q^{22} - 4q^{23} - 4q^{25} + 16q^{26} - 28q^{30} + 24q^{32} + 24q^{33} - 36q^{36} + 22q^{38} - 36q^{40} - 24q^{41} - 18q^{42} - 28q^{47} - 48q^{48} - 6q^{52} + 16q^{55} - 20q^{57} + 52q^{58} - 6q^{60} - 8q^{62} + 48q^{63} - 44q^{66} - 52q^{68} - 6q^{70} - 24q^{71} - 144q^{72} - 4q^{73} + 84q^{76} + 96q^{78} - 42q^{80} + 160q^{81} - 20q^{82} - 120q^{86} - 152q^{87} - 96q^{90} - 8q^{92} + 36q^{95} + 176q^{96} - 12q^{97} + 48q^{98} + O(q^{100}) \)

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.bp.a \(464\) \(6.069\) None \(-6\) \(0\) \(0\) \(-16\)