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Properties

Label 164.1.d
Level $164$
Weight $1$
Character orbit 164.d
Rep. character $\chi_{164}(163,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $21$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 164.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(164, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q - q^{2} + 3 q^{4} - 2 q^{5} - q^{8} + q^{9} - 2 q^{10} + 3 q^{16} - 3 q^{18} - 2 q^{20} - 4 q^{21} + q^{25} - q^{32} - 4 q^{33} + q^{36} - 2 q^{37} - 2 q^{40} + 3 q^{41} + 4 q^{42} + 2 q^{45}+ \cdots - 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(164, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
164.1.d.a 164.d 164.d $1$ $0.082$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) 164.1.d.a \(1\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots\)
164.1.d.b 164.d 164.d $2$ $0.082$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-41}) \) None 164.1.d.b \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots\)