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Properties

Label 959.1.r
Level $959$
Weight $1$
Character orbit 959.r
Rep. character $\chi_{959}(202,\cdot)$
Character field $\Q(\zeta_{34})$
Dimension $16$
Newform subspaces $1$
Sturm bound $92$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 959 = 7 \cdot 137 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 959.r (of order \(34\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 959 \)
Character field: \(\Q(\zeta_{34})\)
Newform subspaces: \( 1 \)
Sturm bound: \(92\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(959, [\chi])\).

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

\( 16 q - 2 q^{2} - 3 q^{4} + q^{7} - 4 q^{8} + q^{9} + O(q^{10}) \) \( 16 q - 2 q^{2} - 3 q^{4} + q^{7} - 4 q^{8} + q^{9} + 2 q^{11} + 2 q^{14} - 5 q^{16} + 2 q^{18} + 4 q^{22} + 17 q^{23} + q^{25} + 3 q^{28} - 6 q^{32} + 3 q^{36} - 2 q^{37} - 11 q^{44} - q^{49} + 2 q^{50} + 4 q^{56} - q^{63} + 10 q^{64} - 17 q^{71} - 13 q^{72} - 4 q^{74} - 2 q^{77} - q^{81} - 9 q^{88} - 2 q^{98} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(959, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
959.1.r.a 959.r 959.r $16$ $0.479$ \(\Q(\zeta_{34})\) $D_{34}$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(1\) \(q+(\zeta_{34}^{10}-\zeta_{34}^{15})q^{2}+(-\zeta_{34}^{3}+\zeta_{34}^{8}+\cdots)q^{4}+\cdots\)