Space of modular forms of level 680, weight 2, and Character 680.cf

• Label: 680.2.cf
• Level: $680$
• Weight: $2$
• Character orbit: 680.cf
• Rep. character: $\chi_{680}(37,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $832$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cf (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 680 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(680, [\chi])\).

	Total	New	Old
Modular forms	896	896	0
Cusp forms	832	832	0
Eisenstein series	64	64	0

Trace form

832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(680, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
680.2.cf.a	$680$	$2$	680.cf	680.bf	$16$	$832$	$104$	$5.430$		None		✓	✓	✓	680.2.cf.a	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{16}]$