Properties

Label 3311.1.bq
Level $3311$
Weight $1$
Character orbit 3311.bq
Rep. character $\chi_{3311}(601,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $2$
Sturm bound $352$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3311 = 7 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3311.bq (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3311 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(352\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3311, [\chi])\).

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

\( 8 q - 6 q^{4} + 2 q^{9} + O(q^{10}) \) \( 8 q - 6 q^{4} + 2 q^{9} + 2 q^{11} + 6 q^{14} + 4 q^{23} + 2 q^{25} + 6 q^{36} - 4 q^{44} - 2 q^{49} + 6 q^{53} - 8 q^{56} - 2 q^{58} - 4 q^{64} - 4 q^{67} + 10 q^{79} - 2 q^{81} - q^{86} - 8 q^{92} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3311, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3311.1.bq.a 3311.bq 3311.aq $4$ $1.652$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
3311.1.bq.b 3311.bq 3311.aq $4$ $1.652$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)