Space of modular forms of level 320, weight 2, and Character 320.bf

• Label: 320.2.bf
• Level: $320$
• Weight: $2$
• Character orbit: 320.bf
• Rep. character: $\chi_{320}(29,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $368$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.bf (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 320 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).

	Total	New	Old
Modular forms	400	400	0
Cusp forms	368	368	0
Eisenstein series	32	32	0

Trace form

\( 368 q - 16 q^{4} - 8 q^{5} - 16 q^{6} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
320.2.bf.a	$320$	$2$	320.bf	320.af	$16$	$368$	$46$	$2.555$		None		✓	✓	✓	320.2.bf.a	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$