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

• Label: 161.4.o
• Level: $161$
• Weight: $4$
• Character orbit: 161.o
• Rep. character: $\chi_{161}(5,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $920$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.o (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{66})\)
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	1000	1000	0
Cusp forms	920	920	0
Eisenstein series	80	80	0

Trace form

920 * q - 11 * q^2 - 27 * q^3 + 157 * q^4 - 33 * q^5 - 22 * q^7 - 104 * q^8 - 359 * q^9 - 33 * q^10 - 11 * q^11 - 75 * q^12 - 22 * q^14 - 44 * q^15 + 1157 * q^16 - 33 * q^17 + 179 * q^18 - 33 * q^19 - 1342 * q^21 - 494 * q^23 - 570 * q^24 + 1269 * q^25 - 609 * q^26 + 682 * q^28 - 348 * q^29 + 1485 * q^30 + 105 * q^31 - 1017 * q^32 - 33 * q^33 + 966 * q^35 + 4354 * q^36 - 1199 * q^37 - 33 * q^38 + 5 * q^39 - 33 * q^40 - 3652 * q^42 - 3476 * q^43 + 3388 * q^44 + 477 * q^46 - 1188 * q^47 - 1408 * q^49 - 3234 * q^50 + 649 * q^51 + 1911 * q^52 - 11 * q^53 - 1659 * q^54 + 9361 * q^56 + 7612 * q^57 - 4198 * q^58 - 915 * q^59 - 11 * q^60 - 33 * q^61 - 2112 * q^63 - 5064 * q^64 - 4323 * q^65 + 858 * q^66 - 11 * q^67 - 2478 * q^70 + 1732 * q^71 - 9181 * q^72 - 3987 * q^73 + 2354 * q^74 + 2871 * q^75 + 2164 * q^77 - 24268 * q^78 + 1837 * q^79 + 12144 * q^80 + 3035 * q^81 + 5823 * q^82 + 11330 * q^84 + 13676 * q^85 + 5225 * q^86 - 24657 * q^87 - 12342 * q^88 - 33 * q^89 + 9810 * q^92 - 1440 * q^93 - 15858 * q^94 - 4187 * q^95 + 2439 * q^96 - 11284 * q^98 + 23056 * q^99

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.o.a	$161$	$4$	161.o	161.o	$66$	$920$	$46$	$9.499$		None		✓	✓	✓	161.4.o.a	$4$	$0$	\(-11\)	\(-27\)	\(-33\)	\(-22\)		$\mathrm{SU}(2)[C_{66}]$