Space of modular forms of level 143, weight 4, and Character 143.s

• Label: 143.4.s
• Level: $143$
• Weight: $4$
• Character orbit: 143.s
• Rep. character: $\chi_{143}(8,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $320$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(143, [\chi])\).

	Total	New	Old
Modular forms	352	352	0
Cusp forms	320	320	0
Eisenstein series	32	32	0

Trace form

\( 320 q - 10 q^{2} - 12 q^{3} - 6 q^{5} - 10 q^{6} - 10 q^{7} - 10 q^{8} - 660 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(143, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
143.4.s.a	$143$	$4$	143.s	143.s	$20$	$320$	$40$	$8.437$		None		$4$	$0$	\(-10\)	\(-12\)	\(-6\)	\(-10\)		$\mathrm{SU}(2)[C_{20}]$