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

• Label: 160.2.o
• Level: $160$
• Weight: $2$
• Character orbit: 160.o
• Rep. character: $\chi_{160}(47,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• 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.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
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	64	16	48
Cusp forms	32	8	24
Eisenstein series	32	8	24

Trace form

\( 8 q + 4 q^{3} + 8 q^{11} - 8 q^{17} - 8 q^{27} - 16 q^{33} - 20 q^{35} - 8 q^{41} - 28 q^{43} - 8 q^{51} + 8 q^{57} + 28 q^{67} + 16 q^{73} + 60 q^{75} + 32 q^{81} + 44 q^{83} + 40 q^{91} + 16 q^{97}+O(q^{100}) \)

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.o.a	$160$	$2$	160.o	40.k	$4$	$8$	$4$	$1.278$	\(\Q(\zeta_{20})\)	None			✓	✓	40.2.k.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_{3} q^{3}+\beta_{5} q^{5}-\beta_{6} q^{7}+(-\beta_{3}+\beta_{2}+\beta_1-1)q^{9}+\cdots\)

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

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