Properties

Label 760.1.bm
Level $760$
Weight $1$
Character orbit 760.bm
Rep. character $\chi_{760}(539,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 760.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(2\)

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 4 4 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - 2 q^{4} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{4} - 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{14} - 2 q^{16} - 2 q^{19} - 2 q^{25} + 8 q^{26} + 2 q^{35} - 2 q^{36} - 2 q^{40} + 2 q^{41} + 2 q^{44} - 4 q^{46} - 4 q^{56} - 4 q^{59} + 4 q^{64} + 8 q^{65} + 2 q^{74} + 4 q^{76} - 2 q^{81} + 2 q^{89} - 2 q^{90} + 4 q^{91} + 8 q^{94} + 2 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
760.1.bm.a 760.bm 760.am $2$ $0.379$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-10}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{7}+q^{8}+\cdots\)
760.1.bm.b 760.bm 760.am $2$ $0.379$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-10}) \) None \(1\) \(0\) \(1\) \(2\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}-q^{8}+\cdots\)