Space of modular forms of level 160, weight 5, and Character 160.h

• Label: 160.5.h
• Level: $160$
• Weight: $5$
• Character orbit: 160.h
• Rep. character: $\chi_{160}(159,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	160.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(160, [\chi])\).

	Total	New	Old
Modular forms	104	24	80
Cusp forms	88	24	64
Eisenstein series	16	0	16

Trace form

\( 24 q + 24 q^{5} + 648 q^{9} - 608 q^{21} - 232 q^{25} + 624 q^{29} - 912 q^{41} - 888 q^{45} + 10888 q^{49} + 4400 q^{61} - 13056 q^{65} + 24736 q^{69} - 9928 q^{81} - 23168 q^{85} - 31824 q^{89}+O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(160, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
160.5.h.a	$160$	$5$	160.h	20.d	$2$	$12$	$12$	$16.539$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			160.5.h.a	$2$	$0$	\(0\)	\(-16\)	\(12\)	\(48\)	$2^{36}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{3}+(1+\beta _{2}-\beta _{6})q^{5}+\cdots\)
160.5.h.b	$160$	$5$	160.h	20.d	$2$	$12$	$12$	$16.539$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			160.5.h.a	$2$	$0$	\(0\)	\(16\)	\(12\)	\(-48\)	$2^{36}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{2})q^{3}+(1+\beta _{2}+\beta _{6})q^{5}+(-4+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(160, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)