Properties

Label 1089.1.i
Level $1089$
Weight $1$
Character orbit 1089.i
Rep. character $\chi_{1089}(122,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1089.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1089, [\chi])\).

Total New Old
Modular forms 26 20 6
Cusp forms 2 2 0
Eisenstein series 24 18 6

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

\( 2q + q^{3} - q^{4} + 3q^{5} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - q^{4} + 3q^{5} - q^{9} + q^{12} + 3q^{15} - q^{16} - 3q^{20} + 2q^{25} - 2q^{27} - q^{31} + 2q^{36} + 2q^{37} - 3q^{47} - 2q^{48} + q^{49} - 3q^{59} + 2q^{64} - q^{67} + 4q^{75} - q^{81} + q^{93} + q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1089.1.i.a \(2\) \(0.543\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(3\) \(0\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)