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

• Label: 143.2.j
• Level: $143$
• Weight: $2$
• Character orbit: 143.j
• Rep. character: $\chi_{143}(23,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	32	20	12
Cusp forms	24	20	4
Eisenstein series	8	0	8

Trace form

\( 20 q + 2 q^{3} + 6 q^{4} - 18 q^{6} - 6 q^{7} - 4 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
143.2.j.a	$143$	$2$	143.j	13.e	$6$	$4$	$2$	$1.142$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(6\)	\(2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
143.2.j.b	$143$	$2$	143.j	13.e	$6$	$16$	$8$	$1.142$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(143, [\chi])\) into lower level spaces

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