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Properties

Label 167.1.b
Level $167$
Weight $1$
Character orbit 167.b
Rep. character $\chi_{167}(166,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 167 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 167.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(167, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 5 5 0
Eisenstein series 1 1 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5 q - q^{2} - q^{3} + 4 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 4 q^{9} - q^{11} - 3 q^{12} - 2 q^{14} + 3 q^{16} - 3 q^{18} - q^{19} - 2 q^{21} - 2 q^{22} - 4 q^{24} + 5 q^{25} - 2 q^{27} - 3 q^{28} - q^{29}+ \cdots - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(167, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
167.1.b.a 167.b 167.b $5$ $0.083$ \(\Q(\zeta_{22})^+\) $D_{11}$ \(\Q(\sqrt{-167}) \) None 167.1.b.a \(-1\) \(-1\) \(0\) \(-1\) \(q+\beta _{4}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)