Properties

Label 760.1.b
Level $760$
Weight $1$
Character orbit 760.b
Rep. character $\chi_{760}(189,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 760.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(760, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 8 q^{9} + O(q^{10}) \) \( 8 q - 8 q^{9} + 8 q^{24} - 8 q^{25} + 8 q^{26} - 8 q^{30} - 8 q^{36} - 8 q^{44} + 8 q^{49} - 8 q^{54} + 8 q^{66} + 8 q^{80} + 8 q^{81} + 8 q^{95} + 8 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(760, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
760.1.b.a 760.b 760.b $8$ $0.379$ \(\Q(\zeta_{16})\) $D_{8}$ \(\Q(\sqrt{-95}) \) None 760.1.b.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)