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

• Label: 161.2.e
• Level: $161$
• Weight: $2$
• Character orbit: 161.e
• Rep. character: $\chi_{161}(93,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	36	28	8
Cusp forms	28	28	0
Eisenstein series	8	0	8

Trace form

28 * q - 2 * q^3 - 12 * q^4 + 8 * q^6 - 2 * q^7 - 12 * q^8 - 16 * q^9 + 10 * q^10 - 4 * q^11 + 6 * q^12 - 8 * q^13 - 4 * q^14 - 12 * q^15 + 10 * q^17 + 10 * q^18 + 2 * q^19 + 8 * q^20 + 2 * q^21 - 40 * q^22 - 20 * q^24 + 2 * q^25 - 28 * q^26 + 16 * q^27 - 30 * q^28 - 4 * q^29 - 8 * q^30 - 4 * q^31 + 2 * q^32 + 22 * q^33 + 32 * q^34 + 6 * q^35 + 80 * q^36 + 6 * q^37 + 10 * q^38 - 12 * q^39 + 24 * q^40 + 28 * q^41 + 26 * q^42 - 4 * q^43 + 14 * q^44 + 2 * q^45 - 16 * q^47 - 68 * q^48 - 36 * q^49 + 28 * q^50 + 12 * q^51 + 20 * q^52 + 10 * q^53 - 22 * q^54 + 4 * q^55 + 16 * q^56 - 56 * q^57 - 10 * q^58 - 14 * q^59 + 4 * q^60 + 12 * q^61 - 48 * q^62 + 8 * q^63 - 68 * q^64 - 22 * q^65 + 10 * q^67 + 40 * q^68 + 16 * q^69 + 50 * q^70 - 16 * q^71 + 52 * q^72 - 26 * q^73 + 34 * q^74 + 4 * q^75 - 28 * q^77 - 68 * q^78 + 14 * q^79 - 8 * q^80 - 30 * q^81 - 60 * q^82 - 68 * q^83 + 12 * q^84 + 52 * q^85 + 22 * q^86 - 14 * q^87 + 46 * q^88 + 10 * q^89 + 28 * q^90 + 18 * q^91 - 26 * q^93 + 32 * q^94 + 28 * q^95 - 88 * q^96 - 32 * q^97 + 10 * q^98 + 128 * 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.e.a	$161$	$2$	161.e	7.c	$3$	$14$	$7$	$1.286$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			161.2.e.a	$2$	$0$	\(0\)	\(-5\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{6}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)
161.2.e.b	$161$	$2$	161.e	7.c	$3$	$14$	$7$	$1.286$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			161.2.e.b	$2$	$0$	\(0\)	\(3\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{12})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)