Space of modular forms of level 79, weight 2, and Character 79.g

• Label: 79.2.g
• Level: $79$
• Weight: $2$
• Character orbit: 79.g
• Rep. character: $\chi_{79}(2,\cdot)$
• Character field: $\Q(\zeta_{39})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $13$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	79.g (of order \(39\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{39})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(13\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(79, [\chi])\).

	Total	New	Old
Modular forms	192	192	0
Cusp forms	144	144	0
Eisenstein series	48	48	0

Trace form

\( 144 q - 24 q^{2} - 26 q^{3} - 22 q^{4} - 25 q^{5} - 35 q^{6} - 26 q^{7} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(79, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
79.2.g.a	$79$	$2$	79.g	79.g	$39$	$144$	$6$	$0.631$		None		$2$	$0$	\(-24\)	\(-26\)	\(-25\)	\(-26\)		$\mathrm{SU}(2)[C_{39}]$