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Properties

Label 760.2.bv
Level $760$
Weight $2$
Character orbit 760.bv
Rep. character $\chi_{760}(217,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $120$
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.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 512 120 392
Cusp forms 448 120 328
Eisenstein series 64 0 64

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 8 q^{11} + 4 q^{23} - 8 q^{25} + 36 q^{33} + 36 q^{41} + 8 q^{43} - 32 q^{45} - 8 q^{47} + 72 q^{51} - 40 q^{55} - 8 q^{57} - 20 q^{63} - 72 q^{67} - 32 q^{73} + 8 q^{77} + 76 q^{81} + 40 q^{83} - 4 q^{85} - 136 q^{87} - 72 q^{91} - 60 q^{93} + 52 q^{95} + O(q^{100}) \)

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.bv.a 760.bv 95.l $120$ $6.069$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)