Space of modular forms of level 2339, weight 1, and Character 2339.b

• Label: 2339.1.b
• Level: $2339$
• Weight: $1$
• Character orbit: 2339.b
• Rep. character: $\chi_{2339}(2338,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $1$
• Sturm bound: $195$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2339 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2339.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2339 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(195\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2339, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	9	9	0
Eisenstein series	1	1	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	9	0	0	0

Trace form

\( 9 q - q^{3} + 9 q^{4} - q^{5} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2339, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2339.1.b.a	$2339$	$1$	2339.b	2339.b	$2$	$9$	$9$	$1.167$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-2339}) \)	None	✓	✓	2339.1.b.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)