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

• Label: 680.2.ci
• Level: $680$
• Weight: $2$
• Character orbit: 680.ci
• Rep. character: $\chi_{680}(11,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $576$
• 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.ci (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
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	576	320
Cusp forms	832	576	256
Eisenstein series	64	0	64

Trace form

576 * q - 16 * q^24 + 32 * q^26 - 96 * q^28 - 80 * q^32 + 64 * q^34 - 64 * q^36 + 80 * q^38 + 96 * q^42 - 32 * q^44 + 16 * q^46 - 80 * q^54 - 80 * q^56 + 64 * q^57 - 112 * q^62 - 96 * q^64 - 208 * q^66 - 208 * q^72 - 96 * q^74 - 112 * q^76 - 64 * q^81 - 80 * q^82 + 128 * q^88 + 224 * q^92 - 192 * q^94 - 272 * 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.ci.a	$680$	$2$	680.ci	136.s	$16$	$576$	$72$	$5.430$		None		✓	✓	✓	680.2.ci.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(680, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)