Space of modular forms of level 161, weight 4, and Character 161.g

• Label: 161.4.g
• Level: $161$
• Weight: $4$
• Character orbit: 161.g
• Rep. character: $\chi_{161}(45,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(161, [\chi])\).

	Total	New	Old
Modular forms	100	100	0
Cusp forms	92	92	0
Eisenstein series	8	8	0

Trace form

92 * q - 6 * q^3 - 168 * q^4 + 60 * q^8 + 348 * q^9 + 42 * q^12 - 728 * q^16 - 102 * q^18 - q^23 + 504 * q^24 - 928 * q^25 + 576 * q^26 + 304 * q^29 - 138 * q^31 - 490 * q^32 + 442 * q^35 + 552 * q^36 - 16 * q^39 - 488 * q^46 + 1122 * q^47 - 792 * q^49 - 660 * q^50 - 1944 * q^52 + 1626 * q^54 - 70 * q^58 + 882 * q^59 + 5020 * q^64 - 3374 * q^70 - 1776 * q^71 + 1184 * q^72 + 3954 * q^73 - 2904 * q^75 - 1966 * q^77 + 4204 * q^78 - 538 * q^81 - 5856 * q^82 - 2940 * q^85 - 3492 * q^87 + 8164 * q^92 + 1418 * q^93 - 9420 * q^94 + 150 * q^95 - 2472 * q^96 + 4310 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(161, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
161.4.g.a	$161$	$4$	161.g	161.g	$6$	$92$	$46$	$9.499$		None		✓	✓	✓	161.4.g.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$