Properties

Label 164.1.l
Level $164$
Weight $1$
Character orbit 164.l
Rep. character $\chi_{164}(23,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
Sturm bound $21$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 164.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

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

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

Trace form

\( 4 q - q^{2} - q^{4} + 2 q^{5} - q^{8} - 4 q^{9} + O(q^{10}) \) \( 4 q - q^{2} - q^{4} + 2 q^{5} - q^{8} - 4 q^{9} + 2 q^{10} - q^{16} + q^{18} - 3 q^{20} - 3 q^{25} - 5 q^{26} + 4 q^{32} + 5 q^{34} + q^{36} - 3 q^{37} + 2 q^{40} - q^{41} - 2 q^{45} + q^{49} + 2 q^{50} + 5 q^{52} - 2 q^{61} - q^{64} + 5 q^{65} + q^{72} + 2 q^{73} - 3 q^{74} - 3 q^{80} + 4 q^{81} - q^{82} - 2 q^{90} - 5 q^{97} + q^{98} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
164.1.l.a 164.l 164.l $4$ $0.082$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(2\) \(0\) \(q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)