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

• Label: 143.4.j
• Level: $143$
• Weight: $4$
• Character orbit: 143.j
• Rep. character: $\chi_{143}(23,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
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	88	72	16
Cusp forms	80	72	8
Eisenstein series	8	0	8

Trace form

\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9} + O(q^{10}) \)

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.j.a	$143$	$4$	143.j	13.e	$6$	$72$	$36$	$8.437$		None		$2$	$0$	\(0\)	\(-12\)	\(0\)	\(-36\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(143, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(143, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)