Space of modular forms of level 161, weight 1, and Character 161.l

• Label: 161.1.l
• Level: $161$
• Weight: $1$
• Character orbit: 161.l
• Rep. character: $\chi_{161}(6,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	161.l (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(161, [\chi])\).

	Total	New	Old
Modular forms	30	30	0
Cusp forms	10	10	0
Eisenstein series	20	20	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

10 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9 - 2 * q^11 - 2 * q^14 + 6 * q^16 - 2 * q^18 - 4 * q^22 - q^23 - q^25 - 3 * q^28 - 2 * q^29 + 5 * q^32 + 8 * q^36 - 2 * q^37 - 2 * q^43 + 5 * q^44 - 2 * q^46 - q^49 + 9 * q^50 - 2 * q^53 - 4 * q^56 + 7 * q^58 - q^63 - 7 * q^64 - 2 * q^67 - 2 * q^71 - 4 * q^72 + 7 * q^74 + 9 * q^77 - 2 * q^79 - q^81 - 4 * q^86 + 3 * q^88 - 3 * q^92 + 9 * q^98 - 2 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(161, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
161.1.l.a	$161$	$1$	161.l	161.l	$22$	$10$	$1$	$0.080$	\(\Q(\zeta_{22})\)	$D_{11}$	\(\Q(\sqrt{-7}) \)	None		✓	✓	✓	161.1.l.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+(-\zeta_{22}+\zeta_{22}^{8})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{5}+\cdots)q^{4}+\cdots\)