Space of modular forms of level 119, weight 1, and Character 119.d

• Label: 119.1.d
• Level: $119$
• Weight: $1$
• Character orbit: 119.d
• Rep. character: $\chi_{119}(118,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	119.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(119, [\chi])\).

	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

\( 4 q - 2 q^{2} + 2 q^{4} - 4 q^{8} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(119, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
119.1.d.a	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-119}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(-1\)	\(2\)	$1$		\(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
119.1.d.b	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-119}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(1\)	\(-2\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots\)