Properties

Label 171.1.o
Level $171$
Weight $1$
Character orbit 171.o
Rep. character $\chi_{171}(94,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 171.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(171, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 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 0 4 0 0

Trace form

\( 4 q - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{9} + 2 q^{11} + 2 q^{16} + 2 q^{23} + 4 q^{24} - 4 q^{26} + 4 q^{30} + 4 q^{35} - 2 q^{38} - 2 q^{39} - 2 q^{42} - 2 q^{43} + 2 q^{45} - 2 q^{47} + 2 q^{54} - 4 q^{55} - 4 q^{57} - 2 q^{58} + 2 q^{61} + 4 q^{62} + 2 q^{63} - 4 q^{64} + 2 q^{66} + 2 q^{77} - 4 q^{80} + 4 q^{81} - 4 q^{82} + 2 q^{83} + 2 q^{87} + 2 q^{93} - 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(171, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
171.1.o.a \(4\) \(0.085\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(-2\) \(-2\) \(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\cdots\)