Space of modular forms of level 161, weight 2, and Character 161.o

• Label: 161.2.o
• Level: $161$
• Weight: $2$
• Character orbit: 161.o
• Rep. character: $\chi_{161}(5,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $280$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(161, [\chi])\).

	Total	New	Old
Modular forms	360	360	0
Cusp forms	280	280	0
Eisenstein series	80	80	0

Trace form

280 * q - 7 * q^2 - 27 * q^3 + q^4 - 33 * q^5 - 22 * q^7 - 56 * q^8 - 15 * q^9 - 33 * q^10 - 11 * q^11 - 39 * q^12 - 22 * q^14 - 44 * q^15 + 11 * q^16 - 33 * q^17 - 77 * q^18 - 33 * q^19 + 44 * q^21 + 11 * q^23 - 30 * q^24 - 11 * q^25 - 21 * q^26 + 66 * q^28 + 33 * q^30 - 33 * q^31 - 27 * q^32 - 33 * q^33 + 10 * q^35 + 66 * q^36 - 55 * q^37 - 33 * q^38 + 5 * q^39 - 33 * q^40 + 88 * q^42 + 44 * q^43 - 66 * q^44 - 29 * q^46 - 30 * q^47 + 16 * q^49 + 26 * q^50 - 55 * q^51 - 105 * q^52 - 11 * q^53 - 3 * q^54 + 99 * q^56 + 44 * q^57 - 36 * q^58 + 21 * q^59 - 11 * q^60 - 33 * q^61 + 33 * q^63 + 24 * q^64 + 66 * q^65 + 66 * q^66 - 11 * q^67 + 6 * q^70 - 60 * q^71 + 59 * q^72 - 15 * q^73 - 129 * q^75 + 13 * q^77 - 252 * q^78 + 33 * q^79 + 264 * q^80 + 99 * q^81 - 33 * q^82 + 44 * q^84 - 212 * q^85 + 11 * q^86 + 381 * q^87 + 198 * q^88 - 33 * q^89 - 214 * q^92 - 12 * q^93 + 180 * q^94 + 32 * q^95 + 51 * q^96 + 80 * q^98 - 198 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(161, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
161.2.o.a	$161$	$2$	161.o	161.o	$66$	$280$	$14$	$1.286$		None		✓	✓	✓	161.2.o.a	$4$	$0$	\(-7\)	\(-27\)	\(-33\)	\(-22\)		$\mathrm{SU}(2)[C_{66}]$