Space of modular forms of level 640, weight 2, and Character 640.bo

• Label: 640.2.bo
• Level: $640$
• Weight: $2$
• Character orbit: 640.bo
• Rep. character: $\chi_{640}(29,\cdot)$
• Character field: $\Q(\zeta_{32})$
• Dimension: $1504$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bo (of order \(32\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 640 \)
Character field:			\(\Q(\zeta_{32})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(640, [\chi])\).

	Total	New	Old
Modular forms	1568	1568	0
Cusp forms	1504	1504	0
Eisenstein series	64	64	0

Trace form

1504 * q - 32 * q^4 - 16 * q^5 - 32 * q^6 - 32 * q^9 - 16 * q^10 - 32 * q^11 - 32 * q^14 - 16 * q^15 - 32 * q^16 - 32 * q^19 - 16 * q^20 - 32 * q^21 - 32 * q^24 - 16 * q^25 - 32 * q^26 - 32 * q^29 - 16 * q^30 - 32 * q^31 - 32 * q^34 - 16 * q^35 - 32 * q^36 - 32 * q^39 - 16 * q^40 - 32 * q^41 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 32 * q^49 - 64 * q^50 - 32 * q^51 - 160 * q^54 - 16 * q^55 + 160 * q^56 - 32 * q^59 - 208 * q^60 - 32 * q^61 - 224 * q^64 + 160 * q^66 - 32 * q^69 - 208 * q^70 - 32 * q^71 - 224 * q^74 - 16 * q^75 + 96 * q^76 - 32 * q^79 - 64 * q^80 - 32 * q^81 - 32 * q^84 - 16 * q^85 - 32 * q^86 - 32 * q^89 - 16 * q^90 - 32 * q^91 - 32 * q^94 - 16 * q^95 - 32 * q^96 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(640, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
640.2.bo.a	$640$	$2$	640.bo	640.ao	$32$	$1504$	$94$	$5.110$		None		✓	✓	✓	640.2.bo.a	$4$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{32}]$