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Properties

Label 1089.1.s
Level $1089$
Weight $1$
Character orbit 1089.s
Rep. character $\chi_{1089}(40,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $24$
Newform subspaces $2$
Sturm bound $132$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1089.s (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 120 88 32
Cusp forms 24 24 0
Eisenstein series 96 64 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 16 0

Trace form

\( 24 q - q^{3} - q^{4} - 3 q^{5} + 3 q^{9} + O(q^{10}) \) \( 24 q - q^{3} - q^{4} - 3 q^{5} + 3 q^{9} - 12 q^{12} + 4 q^{14} + q^{15} - q^{16} + q^{20} - 8 q^{23} + 2 q^{27} + q^{31} + 2 q^{36} + 6 q^{37} - 4 q^{42} - 24 q^{45} - 3 q^{47} - 6 q^{48} - q^{49} - 2 q^{53} - 4 q^{58} + q^{59} + 6 q^{60} - 6 q^{64} + 12 q^{67} + 2 q^{69} - 4 q^{70} + 6 q^{71} - 2 q^{80} + 3 q^{81} + 16 q^{89} + 2 q^{92} - 3 q^{93} + q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.s.a 1089.s 99.o $8$ $0.543$ \(\Q(\zeta_{15})\) $D_{3}$ \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-1\) \(0\) \(q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots\)
1089.1.s.b 1089.s 99.o $16$ $0.543$ 16.0.\(\cdots\).1 $S_{4}$ None None \(0\) \(-2\) \(-2\) \(0\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots\)