Properties

Label 168.1.s
Level $168$
Weight $1$
Character orbit 168.s
Rep. character $\chi_{168}(53,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 168.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(168, [\chi])\).

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

\( 4 q - 2 q^{4} + 4 q^{6} - 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{4} + 4 q^{6} - 2 q^{7} - 2 q^{9} + 2 q^{10} - 4 q^{15} - 2 q^{16} - 4 q^{22} - 2 q^{24} - 2 q^{28} + 2 q^{31} + 2 q^{33} + 4 q^{36} + 2 q^{40} - 2 q^{42} - 2 q^{49} - 2 q^{54} + 4 q^{55} + 2 q^{58} + 2 q^{60} + 4 q^{63} + 4 q^{64} + 2 q^{70} - 4 q^{73} + 2 q^{79} - 2 q^{81} + 2 q^{87} + 2 q^{88} - 4 q^{90} - 2 q^{96} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(168, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
168.1.s.a \(2\) \(0.084\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(1\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
168.1.s.b \(2\) \(0.084\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\)