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

• Label: 160.4.c
• Level: $160$
• Weight: $4$
• Character orbit: 160.c
• Rep. character: $\chi_{160}(129,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	80	18	62
Cusp forms	64	18	46
Eisenstein series	16	0	16

Trace form

\( 18 q - 2 q^{5} - 162 q^{9} + 136 q^{21} - 102 q^{25} - 228 q^{29} - 412 q^{41} + 1074 q^{45} - 1802 q^{49} + 780 q^{61} + 1616 q^{65} + 2504 q^{69} + 218 q^{81} - 3104 q^{85} + 2260 q^{89}+O(q^{100}) \)

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.c.a	$160$	$4$	160.c	5.b	$2$	$2$	$2$	$9.440$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			160.4.c.a	$4$	$0$	\(0\)	\(0\)	\(-22\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta-11)q^{5}+27 q^{9}-46\beta q^{13}+\cdots\)
160.4.c.b	$160$	$4$	160.c	5.b	$2$	$4$	$4$	$9.440$	\(\Q(i, \sqrt{29})\)	None		✓			160.4.c.b	$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-3+\beta _{1})q^{5}+\beta _{2}q^{7}+11q^{9}+\cdots\)
160.4.c.c	$160$	$4$	160.c	5.b	$2$	$4$	$4$	$9.440$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)		✓			160.4.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}+2\beta _{3})q^{3}-5\beta _{2}q^{5}+(-6\beta _{1}+\cdots)q^{7}+\cdots\)
160.4.c.d	$160$	$4$	160.c	5.b	$2$	$8$	$8$	$9.440$	8.0.\(\cdots\).22	None		✓	✓		160.4.c.d	$4$	$0$	\(0\)	\(0\)	\(32\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(4-\beta _{4})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)

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

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