Properties

Label 1169.1.f
Level $1169$
Weight $1$
Character orbit 1169.f
Rep. character $\chi_{1169}(333,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $26$
Newform subspaces $3$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1169 = 7 \cdot 167 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1169.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1169 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(112\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1169, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 26 26 0
Eisenstein series 4 4 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 22 0 4 0

Trace form

\( 26 q - 2 q^{3} - 9 q^{4} - 2 q^{7} - 11 q^{9} + O(q^{10}) \) \( 26 q - 2 q^{3} - 9 q^{4} - 2 q^{7} - 11 q^{9} + 2 q^{11} + 2 q^{12} - 13 q^{16} + 4 q^{21} - 9 q^{25} - 4 q^{27} - 4 q^{28} + 4 q^{29} + 2 q^{31} + 2 q^{33} + 22 q^{36} + 22 q^{42} + 9 q^{44} + 2 q^{47} - 18 q^{48} - 2 q^{49} - 22 q^{54} - 22 q^{62} + 18 q^{64} + 4 q^{65} + 11 q^{72} + 2 q^{75} - 4 q^{77} - 9 q^{81} + 24 q^{84} - 8 q^{85} - 2 q^{87} + 2 q^{89} + 2 q^{93} + 22 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1169, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1169.1.f.a 1169.f 1169.f $2$ $0.583$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-167}) \) None \(-2\) \(1\) \(0\) \(-1\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+3\zeta_{6}^{2}q^{4}-2q^{6}+\cdots\)
1169.1.f.b 1169.f 1169.f $4$ $0.583$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $S_{4}$ None None \(0\) \(-2\) \(0\) \(-2\) \(q+(-1+\beta _{2})q^{3}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
1169.1.f.c 1169.f 1169.f $20$ $0.583$ \(\Q(\zeta_{33})\) $D_{33}$ \(\Q(\sqrt{-167}) \) None \(2\) \(-1\) \(0\) \(1\) \(q+(\zeta_{66}^{16}+\zeta_{66}^{28})q^{2}+(-\zeta_{66}^{9}-\zeta_{66}^{13}+\cdots)q^{3}+\cdots\)