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

• Label: 160.2.n
• Level: $160$
• Weight: $2$
• Character orbit: 160.n
• Rep. character: $\chi_{160}(63,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $6$
• Sturm bound: $48$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(48\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	64	12	52
Cusp forms	32	12	20
Eisenstein series	32	0	32

Trace form

\( 12 q + 4 q^{13} - 12 q^{17} + 16 q^{21} - 12 q^{25} - 16 q^{33} - 20 q^{37} - 16 q^{41} - 20 q^{45} - 52 q^{53} + 32 q^{57} + 44 q^{65} + 28 q^{73} + 48 q^{77} + 36 q^{81} + 68 q^{85} + 80 q^{93} - 36 q^{97}+O(q^{100}) \)

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.n.a	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	\(\Q(\sqrt{-1}) \)	None		✓			160.2.n.a	$2$	$1$	\(0\)	\(-4\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2 i-2)q^{3}+(i-2)q^{5}+(2 i-2)q^{7}+\cdots\)
160.2.n.b	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	\(\Q(\sqrt{-1}) \)	None		✓			160.2.n.b	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{3}+(-2 i+1)q^{5}+(i-1)q^{7}+\cdots\)
160.2.n.c	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	\(\Q(\sqrt{-1}) \)	None		✓			160.2.n.c	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{3}+(2 i+1)q^{5}+(-3 i+3)q^{7}+\cdots\)
160.2.n.d	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	\(\Q(\sqrt{-1}) \)	None		✓			160.2.n.c	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{3}+(2 i+1)q^{5}+(3 i-3)q^{7}+\cdots\)
160.2.n.e	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	\(\Q(\sqrt{-1}) \)	None		✓			160.2.n.b	$2$	$0$	\(0\)	\(2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{3}+(-2 i+1)q^{5}+(-i+1)q^{7}+\cdots\)
160.2.n.f	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	\(\Q(\sqrt{-1}) \)	None		✓			160.2.n.a	$2$	$0$	\(0\)	\(4\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2 i+2)q^{3}+(i-2)q^{5}+(-2 i+2)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(160, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)