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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

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

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.bp.a 760.bp 760.ap $464$ $6.069$ None \(-6\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{12}]$