Properties

Label 1183.1.t
Level $1183$
Weight $1$
Character orbit 1183.t
Rep. character $\chi_{1183}(699,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
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 40 32 8
Cusp forms 12 12 0
Eisenstein series 28 20 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q + 4q^{4} - 6q^{9} + O(q^{10}) \) \( 12q + 4q^{4} - 6q^{9} - 4q^{14} - 2q^{16} + 4q^{22} - 2q^{23} - 12q^{25} + 2q^{29} + 4q^{36} - 2q^{43} + 6q^{49} - 4q^{53} - 4q^{56} + 4q^{74} + 4q^{77} - 4q^{79} - 6q^{81} - 8q^{88} - 12q^{92} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1183.1.t.a \(12\) \(0.590\) 12.0.\(\cdots\).1 \(D_{7}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2}-\beta _{6})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)