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

• 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: $0$

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

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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1089.1.c.a	$1089$	$1$	1089.c	11.b	$2$	$2$	$2$	$0.543$	\(\Q(\sqrt{-2}) \)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	1089.1.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}-\beta q^{19}+\cdots\)