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

• Label: 160.6.c
• Level: $160$
• Weight: $6$
• Character orbit: 160.c
• Rep. character: $\chi_{160}(129,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	128	30	98
Cusp forms	112	30	82
Eisenstein series	16	0	16

Trace form

\( 30 q - 38 q^{5} - 2430 q^{9} + O(q^{10}) \)

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.c.a	$160$	$6$	160.c	5.b	$2$	$2$	$2$	$25.661$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(82\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(41+19i)q^{5}+3^{5}q^{9}-122iq^{13}+\cdots\)
160.6.c.b	$160$	$6$	160.c	5.b	$2$	$4$	$4$	$25.661$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(5\beta _{1}+\beta _{2})q^{3}+5\beta _{3}q^{5}+(46\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
160.6.c.c	$160$	$6$	160.c	5.b	$2$	$12$	$12$	$25.661$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-60\)	\(0\)	$2^{44}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(-5+\beta _{5}+\beta _{8})q^{5}-\beta _{9}q^{7}+\cdots\)
160.6.c.d	$160$	$6$	160.c	5.b	$2$	$12$	$12$	$25.661$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-60\)	\(0\)	$2^{46}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-5+\beta _{5})q^{5}+(-5\beta _{2}-3\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{6}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)