Properties

Label 840.1.cg
Level $840$
Weight $1$
Character orbit 840.cg
Rep. character $\chi_{840}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 840.cg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 840 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(840, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 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

\( 8 q + 4 q^{4} - 8 q^{6} + 4 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{4} - 8 q^{6} + 4 q^{9} + 2 q^{10} - 4 q^{15} - 4 q^{16} - 4 q^{24} - 2 q^{25} - 4 q^{31} + 8 q^{36} - 2 q^{40} - 4 q^{49} - 4 q^{54} + 12 q^{55} - 2 q^{60} - 8 q^{64} - 6 q^{70} + 4 q^{79} - 4 q^{81} + 4 q^{90} + 4 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(840, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
840.1.cg.a 840.cg 840.bg $4$ $0.419$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
840.1.cg.b 840.cg 840.bg $4$ $0.419$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)