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

• Label: 161.2.m
• Level: $161$
• Weight: $2$
• Character orbit: 161.m
• Rep. character: $\chi_{161}(2,\cdot)$
• Character field: $\Q(\zeta_{33})$
• 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.m (of order \(33\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{33})\)
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 - 11 * q^2 - 9 * q^3 + q^4 - 11 * q^5 - 52 * q^6 - 20 * q^7 - 32 * q^8 + 5 * q^9 - 21 * q^10 - 7 * q^11 - 17 * q^12 - 36 * q^13 - 18 * q^14 - 32 * q^15 + 11 * q^16 - 21 * q^17 + 23 * q^18 - 13 * q^19 + 36 * q^20 - 90 * q^21 - 48 * q^22 + 11 * q^23 - 2 * q^24 + 9 * q^25 + 17 * q^26 + 6 * q^27 - 80 * q^28 - 40 * q^29 + 41 * q^30 - 7 * q^31 + 9 * q^32 - 33 * q^33 - 76 * q^34 - 6 * q^35 - 234 * q^36 + 27 * q^37 + 89 * q^38 + q^39 - 35 * q^40 - 72 * q^41 + 62 * q^42 - 128 * q^43 + 30 * q^44 + 108 * q^45 - 11 * q^46 - 6 * q^47 + 68 * q^48 + 80 * q^49 - 226 * q^50 + 21 * q^51 + 189 * q^52 - 21 * q^53 + 55 * q^54 - 48 * q^55 + 83 * q^56 - 76 * q^57 + 10 * q^58 + 47 * q^59 - 15 * q^60 + 65 * q^61 + 4 * q^62 + 25 * q^63 + 24 * q^64 - 66 * q^65 - 44 * q^66 - 21 * q^67 + 202 * q^68 - 60 * q^69 - 6 * q^70 - 28 * q^71 - 129 * q^72 + 15 * q^73 - 34 * q^74 + 139 * q^75 - 44 * q^76 + 61 * q^77 + 244 * q^78 - 69 * q^79 - 102 * q^80 + 151 * q^81 + 137 * q^82 + 24 * q^83 + 32 * q^84 + 124 * q^85 - 55 * q^86 - 129 * q^87 + 64 * q^88 - 21 * q^89 - 28 * q^90 - 62 * q^91 + 154 * q^92 + 4 * q^93 - 98 * q^94 + 38 * q^95 + 165 * q^96 - 12 * q^97 + 12 * q^98 + 202 * 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.m.a	$161$	$2$	161.m	161.m	$33$	$280$	$14$	$1.286$		None		✓	✓	✓	161.2.m.a	$4$	$0$	\(-11\)	\(-9\)	\(-11\)	\(-20\)		$\mathrm{SU}(2)[C_{33}]$