Space of modular forms of level 143, weight 2, and Character 143.s

• Label: 143.2.s
• Level: $143$
• Weight: $2$
• Character orbit: 143.s
• Rep. character: $\chi_{143}(8,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.s (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 143 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(143, [\chi])\).

	Total	New	Old
Modular forms	128	128	0
Cusp forms	96	96	0
Eisenstein series	32	32	0

Trace form

96 * q - 10 * q^2 - 12 * q^3 - 6 * q^5 - 10 * q^6 - 10 * q^7 - 10 * q^8 - 28 * q^9 + 8 * q^11 - 20 * q^13 + 12 * q^14 + 10 * q^15 + 24 * q^16 - 10 * q^18 - 10 * q^19 + 4 * q^20 - 32 * q^22 - 50 * q^24 - 34 * q^26 - 12 * q^27 - 10 * q^28 + 18 * q^31 - 48 * q^33 + 44 * q^34 + 80 * q^35 - 18 * q^37 - 90 * q^39 - 100 * q^40 + 50 * q^41 - 56 * q^42 - 14 * q^44 + 60 * q^45 + 50 * q^46 + 28 * q^47 + 152 * q^48 - 60 * q^50 - 60 * q^52 - 24 * q^53 + 28 * q^55 - 10 * q^57 + 14 * q^58 + 4 * q^59 + 32 * q^60 + 20 * q^61 - 60 * q^63 + 116 * q^66 - 100 * q^67 - 80 * q^68 + 26 * q^71 + 170 * q^72 - 40 * q^73 - 20 * q^74 + 196 * q^78 + 60 * q^79 - 82 * q^80 - 68 * q^81 - 110 * q^83 + 220 * q^84 + 30 * q^85 - 22 * q^86 + 48 * q^89 + 38 * q^91 + 48 * q^92 + 60 * q^93 + 160 * q^94 - 160 * q^96 - 40 * q^97 + 70 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(143, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
143.2.s.a	$143$	$2$	143.s	143.s	$20$	$96$	$12$	$1.142$		None		✓	✓	✓	143.2.s.a	$4$	$0$	\(-10\)	\(-12\)	\(-6\)	\(-10\)		$\mathrm{SU}(2)[C_{20}]$