Space of modular forms of level 160, weight 2, and Character 160.x

• Label: 160.2.x
• Level: $160$
• Weight: $2$
• Character orbit: 160.x
• Rep. character: $\chi_{160}(21,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.x (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(160, [\chi])\).

	Total	New	Old
Modular forms	104	64	40
Cusp forms	88	64	24
Eisenstein series	16	0	16

Trace form

64 * q - 8 * q^10 - 16 * q^14 - 40 * q^16 - 40 * q^18 - 16 * q^20 + 8 * q^22 - 16 * q^23 + 32 * q^24 - 48 * q^27 + 40 * q^28 + 40 * q^32 + 40 * q^34 - 24 * q^36 + 40 * q^38 - 48 * q^39 - 40 * q^42 - 16 * q^43 - 80 * q^44 - 64 * q^46 + 16 * q^51 - 16 * q^52 - 32 * q^53 - 56 * q^54 - 72 * q^56 + 72 * q^58 + 32 * q^59 - 32 * q^61 + 24 * q^62 + 80 * q^63 + 48 * q^64 + 16 * q^66 + 80 * q^67 + 48 * q^68 - 32 * q^69 + 32 * q^71 + 72 * q^72 + 8 * q^74 - 32 * q^77 + 72 * q^78 + 32 * q^80 - 80 * q^83 + 56 * q^84 + 72 * q^86 + 80 * q^88 + 72 * q^90 - 96 * q^91 - 8 * q^92 - 40 * q^94 - 64 * q^95 + 104 * q^96 + 80 * q^98 - 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(160, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
160.2.x.a	$160$	$2$	160.x	32.g	$8$	$64$	$16$	$1.278$		None		✓	✓	✓	160.2.x.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(160, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)