Properties

Label 1089.1.c
Level $1089$
Weight $1$
Character orbit 1089.c
Rep. character $\chi_{1089}(604,\cdot)$
Character field $\Q$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
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 6 20
Cusp forms 2 2 0
Eisenstein series 24 4 20

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

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

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1089.1.c.a 1089.c 11.b $2$ $0.543$ \(\Q(\sqrt{-2}) \) $D_{4}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}-\beta q^{19}+\cdots\)