Space of modular forms of level 160, weight 3, and Character 160.p

• Label: 160.3.p
• Level: $160$
• Weight: $3$
• Character orbit: 160.p
• Rep. character: $\chi_{160}(33,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $72$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	160.p (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(72\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(160, [\chi])\).

	Total	New	Old
Modular forms	112	24	88
Cusp forms	80	24	56
Eisenstein series	32	0	32

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(160, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
160.3.p.a	$160$	$3$	160.p	5.c	$4$	$2$	$1$	$4.360$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-4+3i)q^{5}+9iq^{9}+(-17+17i)q^{13}+\cdots\)
160.3.p.b	$160$	$3$	160.p	5.c	$4$	$2$	$1$	$4.360$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(4+3i)q^{5}+9iq^{9}+(7-7i)q^{13}+\cdots\)
160.3.p.c	$160$	$3$	160.p	5.c	$4$	$4$	$2$	$4.360$	\(\Q(i, \sqrt{15})\)	None		$4$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}-5q^{5}+\beta _{3}q^{7}+21\beta _{1}q^{9}+\cdots\)
160.3.p.d	$160$	$3$	160.p	5.c	$4$	$4$	$2$	$4.360$	\(\Q(i, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}+(3+4\beta _{1})q^{5}-3\beta _{3}q^{7}+5\beta _{1}q^{9}+\cdots\)
160.3.p.e	$160$	$3$	160.p	5.c	$4$	$6$	$3$	$4.360$	6.0.3534400.1	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots\)
160.3.p.f	$160$	$3$	160.p	5.c	$4$	$6$	$3$	$4.360$	6.0.3534400.1	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(2+2\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

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