Space of modular forms of level 431, weight 2, and Character 431.g

• Label: 431.2.g
• Level: $431$
• Weight: $2$
• Character orbit: 431.g
• Rep. character: $\chi_{431}(5,\cdot)$
• Character field: $\Q(\zeta_{215})$
• Dimension: $5880$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	431.g (of order \(215\) and degree \(168\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 431 \)
Character field:			\(\Q(\zeta_{215})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(431, [\chi])\).

	Total	New	Old
Modular forms	6216	6216	0
Cusp forms	5880	5880	0
Eisenstein series	336	336	0

Trace form

\( 5880 q - 166 q^{2} - 164 q^{3} - 302 q^{4} - 169 q^{5} - 148 q^{6} - 171 q^{7} - 160 q^{8} - 300 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(431, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
431.2.g.a	$431$	$2$	431.g	431.g	$215$	$5880$	$35$	$3.442$		None		✓	431.2.g.a	$2$	$0$	\(-166\)	\(-164\)	\(-169\)	\(-171\)		$\mathrm{SU}(2)[C_{215}]$