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

\( 3q - q^{2} + 3q^{4} - 2q^{5} - q^{8} + q^{9} + O(q^{10}) \) \( 3q - q^{2} + 3q^{4} - 2q^{5} - q^{8} + q^{9} - 2q^{10} + 3q^{16} - 3q^{18} - 2q^{20} - 4q^{21} + q^{25} - q^{32} - 4q^{33} + q^{36} - 2q^{37} - 2q^{40} + 3q^{41} + 4q^{42} + 2q^{45} + q^{49} + 5q^{50} + 4q^{57} - 2q^{61} + 3q^{64} + 4q^{66} - 3q^{72} - 2q^{73} - 2q^{74} + 4q^{77} - 2q^{80} - q^{81} - q^{82} - 4q^{84} + 2q^{90} - 3q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
164.1.d.a \(1\) \(0.082\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(1\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots\)
164.1.d.b \(2\) \(0.082\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots\)