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Properties

Label 3311.1.bm
Level $3311$
Weight $1$
Character orbit 3311.bm
Rep. character $\chi_{3311}(1770,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3311 \)
Character field: \(\Q(\zeta_{6})\)
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 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

\( 4 q + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{9} - 4 q^{11} + 2 q^{14} - 4 q^{16} - 2 q^{23} + 2 q^{25} - 2 q^{49} - 4 q^{53} - 2 q^{56} + 2 q^{58} + 4 q^{64} + 2 q^{67} + 6 q^{71} - 2 q^{81} - 2 q^{86} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bm.a 3311.bm 3311.am $2$ $1.652$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q-q^{2}-\zeta_{6}q^{7}+q^{8}+\zeta_{6}q^{9}-q^{11}+\cdots\)
3311.1.bm.b 3311.bm 3311.am $2$ $1.652$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+q^{2}+\zeta_{6}q^{7}-q^{8}+\zeta_{6}q^{9}-q^{11}+\cdots\)