Space of modular forms of level 160, weight 4, and Character 160.f

• Label: 160.4.f
• Level: $160$
• Weight: $4$
• Character orbit: 160.f
• Rep. character: $\chi_{160}(49,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(160, [\chi])\).

	Total	New	Old
Modular forms	80	20	60
Cusp forms	64	16	48
Eisenstein series	16	4	12

Trace form

\( 16 q + 104 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(160, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
160.4.f.a	$160$	$4$	160.f	40.f	$2$	$16$	$16$	$9.440$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓	✓	40.4.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{40}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}+\beta _{6}q^{5}-\beta _{9}q^{7}+(6-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

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