Space of modular forms of level 160, weight 6, and Character 160.n

• Label: 160.6.n
• Level: $160$
• Weight: $6$
• Character orbit: 160.n
• Rep. character: $\chi_{160}(63,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(160, [\chi])\).

	Total	New	Old
Modular forms	256	60	196
Cusp forms	224	60	164
Eisenstein series	32	0	32

Trace form

\( 60 q + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(160, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
160.6.n.a	$160$	$6$	160.n	20.e	$4$	$14$	$7$	$25.661$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(-10\)	\(42\)	\(-66\)	$2^{31}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{1}+\beta _{2})q^{3}+(3-4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
160.6.n.b	$160$	$6$	160.n	20.e	$4$	$14$	$7$	$25.661$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(10\)	\(42\)	\(66\)	$2^{31}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1}-\beta _{2})q^{3}+(3-4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
160.6.n.c	$160$	$6$	160.n	20.e	$4$	$16$	$8$	$25.661$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(-10\)	\(-42\)	\(86\)	$2^{41}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{3}-\beta _{4})q^{3}+(-3+\beta _{4}-\beta _{8}+\cdots)q^{5}+\cdots\)
160.6.n.d	$160$	$6$	160.n	20.e	$4$	$16$	$8$	$25.661$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(10\)	\(-42\)	\(-86\)	$2^{41}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{3}+\beta _{4})q^{3}+(-3+\beta _{4}-\beta _{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)