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

• Label: 160.2.d
• Level: $160$
• Weight: $2$
• Character orbit: 160.d
• Rep. character: $\chi_{160}(81,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
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	32	4	28
Cusp forms	16	4	12
Eisenstein series	16	0	16

Trace form

4 * q + 4 * q^7 - 4 * q^9 - 4 * q^15 + 4 * q^23 - 4 * q^25 + 8 * q^31 + 8 * q^33 - 24 * q^39 - 8 * q^41 - 20 * q^47 - 12 * q^49 + 8 * q^55 + 8 * q^57 + 20 * q^63 - 8 * q^71 + 16 * q^73 + 32 * q^79 + 4 * q^81 + 48 * q^87 + 8 * q^89 - 16 * q^95 - 16 * q^97

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.d.a	$160$	$2$	160.d	8.b	$2$	$4$	$4$	$1.278$	\(\Q(\zeta_{12})\)	None			✓	✓	40.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{3}+\beta_1 q^{5}+(\beta_{3}+1)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(160, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)