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

• Label: 161.2.i
• Level: $161$
• Weight: $2$
• Character orbit: 161.i
• Rep. character: $\chi_{161}(8,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	180	120	60
Cusp forms	140	120	20
Eisenstein series	40	0	40

Trace form

120 * q - 2 * q^2 - 4 * q^3 - 22 * q^4 - 4 * q^5 - 14 * q^6 - 2 * q^7 - 12 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 - 22 * q^12 - 12 * q^13 - 6 * q^14 - 22 * q^15 - 28 * q^16 + 14 * q^17 + 20 * q^18 - 6 * q^19 - 36 * q^20 - 4 * q^21 + 4 * q^23 + 96 * q^24 - 22 * q^25 + 10 * q^26 - 52 * q^27 - 14 * q^28 - 6 * q^29 + 20 * q^30 - 34 * q^31 - 24 * q^32 - 2 * q^33 - 12 * q^34 - 4 * q^35 - 21 * q^36 + 8 * q^37 - 16 * q^38 + 24 * q^39 + 108 * q^40 + 16 * q^41 - 4 * q^42 + 12 * q^43 + 17 * q^44 - 72 * q^45 + 108 * q^46 + 24 * q^47 + 34 * q^48 - 12 * q^49 - 25 * q^50 - 20 * q^51 - 98 * q^52 - 40 * q^53 + 50 * q^54 + 56 * q^55 - 30 * q^56 + 26 * q^57 - 39 * q^58 + 28 * q^59 + 76 * q^60 - 56 * q^61 + 42 * q^62 - 26 * q^63 - 52 * q^65 + 28 * q^66 - 48 * q^67 - 160 * q^68 + 14 * q^69 - 8 * q^70 + 38 * q^71 - 164 * q^72 - 8 * q^73 + 35 * q^74 - 8 * q^75 + 82 * q^76 + 36 * q^77 - 86 * q^78 - 36 * q^79 + 68 * q^80 + 96 * q^81 + 26 * q^82 + 42 * q^83 + 114 * q^84 - 44 * q^85 + 44 * q^86 - 92 * q^87 - 133 * q^88 + 52 * q^89 + 146 * q^90 + 72 * q^91 - 156 * q^92 + 132 * q^93 - 122 * q^94 - 56 * q^95 + 252 * q^96 + 122 * q^97 + 9 * q^98 - 136 * 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.i.a	$161$	$2$	161.i	23.c	$11$	$50$	$5$	$1.286$		None		✓			161.2.i.a	$2$	$0$	\(2\)	\(0\)	\(-11\)	\(5\)		$\mathrm{SU}(2)[C_{11}]$
161.2.i.b	$161$	$2$	161.i	23.c	$11$	$70$	$7$	$1.286$		None		✓	✓		161.2.i.b	$2$	$0$	\(-4\)	\(-4\)	\(7\)	\(-7\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(161, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(161, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)