Space of modular forms of level 597, weight 1, and Character 597.g

• Label: 597.1.g
• Level: $597$
• Weight: $1$
• Character orbit: 597.g
• Rep. character: $\chi_{597}(92,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $66$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 597 = 3 \cdot 199 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	597.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 597 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(66\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(597, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	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	2	0	0	0

Trace form

\( 2 q - q^{3} - q^{4} + q^{7} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(597, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
597.1.g.a	$597$	$1$	597.g	597.g	$6$	$2$	$1$	$0.298$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	597.1.g.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)