Space of modular forms of level 86, weight 2, and Character 86.g

• Label: 86.2.g
• Level: $86$
• Weight: $2$
• Character orbit: 86.g
• Rep. character: $\chi_{86}(9,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 86 = 2 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	86.g (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(86, [\chi])\).

	Total	New	Old
Modular forms	156	36	120
Cusp forms	108	36	72
Eisenstein series	48	0	48

Trace form

\( 36 q - 2 q^{2} + 2 q^{3} - 6 q^{4} + 6 q^{5} + 2 q^{7} - 2 q^{8} - 13 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(86, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
86.2.g.a	$86$	$2$	86.g	43.g	$21$	$12$	$1$	$0.687$	\(\Q(\zeta_{21})\)	None		$2$	$0$	\(2\)	\(8\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{21}]$	\(q+(1-\zeta_{21}+\zeta_{21}^{3}-\zeta_{21}^{4}+\zeta_{21}^{6}+\cdots)q^{2}+\cdots\)
86.2.g.b	$86$	$2$	86.g	43.g	$21$	$24$	$2$	$0.687$		None		$2$	$0$	\(-4\)	\(-6\)	\(3\)	\(3\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(86, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(86, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 2}\)