Properties

Label 1183.1.x
Level $1183$
Weight $1$
Character orbit 1183.x
Rep. character $\chi_{1183}(319,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $8$
Newform subspaces $1$
Sturm bound $121$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1183.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(121\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1183, [\chi])\).

Total New Old
Modular forms 64 48 16
Cusp forms 8 8 0
Eisenstein series 56 40 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 8 0 0

Trace form

\( 8 q - 4 q^{3} + O(q^{10}) \) \( 8 q - 4 q^{3} - 4 q^{14} + 8 q^{16} + 4 q^{22} - 8 q^{27} + 4 q^{35} + 4 q^{40} - 4 q^{42} - 4 q^{48} - 4 q^{53} - 4 q^{55} - 4 q^{61} + 4 q^{66} - 8 q^{74} + 4 q^{79} + 4 q^{81} - 4 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1183, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1183.1.x.a 1183.x 91.x $8$ $0.590$ \(\Q(\zeta_{24})\) $A_{4}$ None None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{7}q^{5}+\cdots\)