Space of modular forms of level 159, weight 1, and Character 159.d

• Label: 159.1.d
• Level: $159$
• Weight: $1$
• Character orbit: 159.d
• Rep. character: $\chi_{159}(158,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 159 = 3 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	159.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 159 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(159, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	4	4	0
Eisenstein series	2	2	0

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

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

Trace form

\( 4 q + 2 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(159, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
159.1.d.a	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-159}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots\)
159.1.d.b	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-159}) \)	None	✓	$2$	$0$	\(1\)	\(-2\)	\(1\)	\(-1\)	$1$		\(q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+\beta q^{5}+\cdots\)