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Properties

Label 3311.1.co
Level $3311$
Weight $1$
Character orbit 3311.co
Rep. character $\chi_{3311}(811,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $16$
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.co (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3311 \)
Character field: \(\Q(\zeta_{30})\)
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 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q - 2 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{9} + 4 q^{11} + 3 q^{14} - 6 q^{16} + 15 q^{18} + 2 q^{23} - 2 q^{25} + 15 q^{28} + 10 q^{44} - 15 q^{46} + 2 q^{49} - 6 q^{53} + 2 q^{56} - 7 q^{58} - 14 q^{64} - 2 q^{67} + 9 q^{71} + 5 q^{79} + 2 q^{81} - 8 q^{86} - 10 q^{92} - 8 q^{99} + O(q^{100}) \)

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.co.a 3311.co 3311.bo $8$ $1.652$ \(\Q(\zeta_{15})\) $D_{30}$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{30}-\zeta_{30}^{2})q^{2}+(\zeta_{30}^{2}-\zeta_{30}^{3}+\cdots)q^{4}+\cdots\)
3311.1.co.b 3311.co 3311.bo $8$ $1.652$ \(\Q(\zeta_{15})\) $D_{30}$ \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+(-\zeta_{30}^{7}-\zeta_{30}^{11})q^{2}+(-\zeta_{30}^{3}+\cdots)q^{4}+\cdots\)