Properties

Label 1089.1.h
Level $1089$
Weight $1$
Character orbit 1089.h
Rep. character $\chi_{1089}(241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
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 32 20 12
Cusp forms 8 4 4
Eisenstein series 24 16 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 4 0

Trace form

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

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.h.a \(4\) \(0.543\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(S_{4}\) None None \(0\) \(2\) \(2\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)