Space of modular forms of level 139, weight 2, and Character 139.g

• Label: 139.2.g
• Level: $139$
• Weight: $2$
• Character orbit: 139.g
• Rep. character: $\chi_{139}(4,\cdot)$
• Character field: $\Q(\zeta_{69})$
• Dimension: $484$
• Newform subspaces: $1$
• Sturm bound: $23$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	139.g (of order \(69\) and degree \(44\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 139 \)
Character field:			\(\Q(\zeta_{69})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(23\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(139, [\chi])\).

	Total	New	Old
Modular forms	572	572	0
Cusp forms	484	484	0
Eisenstein series	88	88	0

Trace form

\( 484 q - 46 q^{2} - 48 q^{3} - 32 q^{4} - 44 q^{5} - 52 q^{6} - 45 q^{7} - 46 q^{8} - 41 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(139, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
139.2.g.a	$139$	$2$	139.g	139.g	$69$	$484$	$11$	$1.110$		None		$2$	$0$	\(-46\)	\(-48\)	\(-44\)	\(-45\)		$\mathrm{SU}(2)[C_{69}]$