Space of modular forms of level 1589, weight 1, and Character 1589.g

• Label: 1589.1.g
• Level: $1589$
• Weight: $1$
• Character orbit: 1589.g
• Rep. character: $\chi_{1589}(226,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $152$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1589 = 7 \cdot 227 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1589.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1589 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(152\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1589, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(1589, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1589.1.g.a	$1589$	$1$	1589.g	1589.g	$6$	$2$	$1$	$0.793$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-227}) \)	None		✓	1589.1.g.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}^{2}q^{11}+\cdots\)
1589.1.g.b	$1589$	$1$	1589.g	1589.g	$6$	$8$	$4$	$0.793$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-227}) \)	None		✓	1589.1.g.b	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{3}-\zeta_{30}^{5}q^{4}+\zeta_{30}^{8}q^{7}+\cdots\)