Space of modular forms of level 1089, weight 1, and Character 1089.h

• 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: $0$

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

\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1089.1.h.a	$1089$	$1$	1089.h	99.h	$6$	$4$	$2$	$0.543$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$		\(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)

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

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