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 - 8 * q^10 - 16 * q^11 - 16 * q^14 - 8 * q^15 - 16 * q^16 - 16 * q^19 - 8 * q^20 - 16 * q^21 - 16 * q^24 - 8 * q^25 - 96 * q^26 - 16 * q^29 + 72 * q^30 - 16 * q^34 - 8 * q^35 - 176 * q^36 - 16 * q^39 + 32 * q^40 - 16 * q^41 - 16 * q^44 - 8 * q^45 - 16 * q^46 - 16 * q^49 + 16 * q^50 + 16 * q^51 + 48 * q^54 - 72 * q^55 - 112 * q^56 - 80 * q^59 + 88 * q^60 - 16 * q^61 + 80 * q^64 - 16 * q^65 - 144 * q^66 - 16 * q^69 + 88 * q^70 + 48 * q^71 + 80 * q^74 - 72 * q^75 - 80 * q^76 - 48 * q^79 + 16 * q^80 - 16 * q^81 - 128 * q^84 - 8 * q^85 - 16 * q^86 - 16 * q^89 - 8 * q^90 - 16 * q^91 - 192 * q^94 - 16 * q^96 - 64 * q^99

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	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$