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

• Label: 160.4.ba
• Level: $160$
• Weight: $4$
• Character orbit: 160.ba
• Rep. character: $\chi_{160}(3,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $280$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.ba (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 160 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	296	296	0
Cusp forms	280	280	0
Eisenstein series	16	16	0

Trace form

280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 - 88 * q^8 - 16 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 - 64 * q^14 - 8 * q^15 - 8 * q^16 - 36 * q^18 + 48 * q^19 + 304 * q^20 - 8 * q^21 - 436 * q^22 - 8 * q^23 - 736 * q^24 - 4 * q^25 - 8 * q^26 + 104 * q^27 - 260 * q^28 - 632 * q^30 + 336 * q^32 - 8 * q^33 - 696 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 2244 * q^38 + 816 * q^40 - 8 * q^41 + 452 * q^42 - 868 * q^43 - 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 1384 * q^48 + 11368 * q^49 + 28 * q^50 + 1480 * q^51 + 320 * q^52 - 4 * q^53 - 2968 * q^54 + 284 * q^55 - 344 * q^56 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 + 496 * q^62 - 2744 * q^63 - 816 * q^64 - 8 * q^65 + 552 * q^66 - 1852 * q^67 + 1224 * q^68 - 216 * q^69 - 980 * q^70 - 232 * q^71 + 664 * q^72 - 112 * q^75 + 824 * q^76 - 1376 * q^77 - 5744 * q^78 - 4528 * q^80 + 524 * q^82 - 2684 * q^83 - 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 5256 * q^88 + 2068 * q^90 - 8 * q^91 - 3796 * q^92 + 104 * q^93 - 416 * q^94 + 6168 * q^96 - 8 * q^97 + 2760 * q^98

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.ba.a	$160$	$4$	160.ba	160.aa	$8$	$280$	$70$	$9.440$		None		✓	✓	✓	160.4.u.a	$2$	$0$	\(-4\)	\(-4\)	\(-4\)	\(-8\)		$\mathrm{SU}(2)[C_{8}]$