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Properties

Label 189.1.q
Level $189$
Weight $1$
Character orbit 189.q
Rep. character $\chi_{189}(53,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 189.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(189, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - q^{4} + 2q^{7} + O(q^{10}) \) \( 2q - q^{4} + 2q^{7} - 2q^{13} - q^{16} - 2q^{19} - q^{25} - q^{28} + q^{31} + q^{37} - 2q^{43} + 2q^{49} + q^{52} + q^{61} + 2q^{64} + q^{67} - 2q^{73} + 4q^{76} + q^{79} - 2q^{91} - 2q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
189.1.q.a \(2\) \(0.094\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{6}^{2}q^{4}+q^{7}-q^{13}-\zeta_{6}q^{16}-\zeta_{6}q^{19}+\cdots\)