Properties

Label 1089.1.k
Level $1089$
Weight $1$
Character orbit 1089.k
Rep. character $\chi_{1089}(118,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
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.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
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 104 24 80
Cusp forms 8 8 0
Eisenstein series 96 16 80

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q - 2q^{4} + O(q^{10}) \) \( 8q - 2q^{4} - 2q^{16} + 2q^{25} + 2q^{49} - 2q^{64} - 4q^{91} + 4q^{97} + O(q^{100}) \)

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.k.a \(8\) \(0.543\) 8.0.64000000.1 \(D_{4}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{4}-\beta _{7}q^{7}-\beta _{1}q^{13}+\beta _{4}q^{16}+\cdots\)