Space of modular forms of level 731, weight 2, and Character 731.z

• Label: 731.2.z
• Level: $731$
• Weight: $2$
• Character orbit: 731.z
• Rep. character: $\chi_{731}(67,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $768$
• Newform subspaces: $1$
• Sturm bound: $132$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.z (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 731 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(132\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

	Total	New	Old
Modular forms	816	816	0
Cusp forms	768	768	0
Eisenstein series	48	48	0

Trace form

\( 768 q - 24 q^{2} - 144 q^{4} - 16 q^{8} - 98 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
731.2.z.a	$731$	$2$	731.z	731.z	$42$	$768$	$64$	$5.837$		None		✓	✓	✓	731.2.z.a	$4$	$0$	\(-24\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{42}]$