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Properties

Label 1656.1.z
Level $1656$
Weight $1$
Character orbit 1656.z
Rep. character $\chi_{1656}(275,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $288$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1656.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1656 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1656, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 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 12 0 0 0

Trace form

\( 12 q + 3 q^{6} + O(q^{10}) \) \( 12 q + 3 q^{6} - 6 q^{12} + 3 q^{18} - 6 q^{25} + 6 q^{27} - 3 q^{36} - 6 q^{48} + 6 q^{49} + 3 q^{52} - 3 q^{58} - 18 q^{59} - 6 q^{64} - 3 q^{78} - 6 q^{82} - 3 q^{94} - 3 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1656, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1656.1.z.a 1656.z 1656.z $6$ $0.826$ \(\Q(\zeta_{18})\) $D_{18}$ \(\Q(\sqrt{-23}) \) None 1656.1.z.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{5}q^{3}+\zeta_{18}^{4}q^{4}+\cdots\)
1656.1.z.b 1656.z 1656.z $6$ $0.826$ \(\Q(\zeta_{18})\) $D_{18}$ \(\Q(\sqrt{-23}) \) None 1656.1.z.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{4}q^{2}-\zeta_{18}^{2}q^{3}+\zeta_{18}^{8}q^{4}+\cdots\)