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

\( 12 q + O(q^{10}) \)

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

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

\( S_{2}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)