Space of modular forms of level 859, weight 2, and Character 859.j

• Label: 859.2.j
• Level: $859$
• Weight: $2$
• Character orbit: 859.j
• Rep. character: $\chi_{859}(33,\cdot)$
• Character field: $\Q(\zeta_{39})$
• Dimension: $1704$
• Newform subspaces: $1$
• Sturm bound: $143$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	859.j (of order \(39\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 859 \)
Character field:			\(\Q(\zeta_{39})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(143\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(859, [\chi])\).

	Total	New	Old
Modular forms	1752	1752	0
Cusp forms	1704	1704	0
Eisenstein series	48	48	0

Trace form

\( 1704 q - 26 q^{2} - 24 q^{3} + 48 q^{4} - 49 q^{5} - 38 q^{6} - 22 q^{7} - 8 q^{8} + 49 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(859, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
859.2.j.a	$859$	$2$	859.j	859.j	$39$	$1704$	$71$	$6.859$		None		$2$	$0$	\(-26\)	\(-24\)	\(-49\)	\(-22\)		$\mathrm{SU}(2)[C_{39}]$