Space of modular forms of level 119, weight 2, and Character 119.g

• Label: 119.2.g
• Level: $119$
• Weight: $2$
• Character orbit: 119.g
• Rep. character: $\chi_{119}(64,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	119.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(119, [\chi])\).

	Total	New	Old
Modular forms	28	20	8
Cusp forms	20	20	0
Eisenstein series	8	0	8

Trace form

\( 20 q - 4 q^{3} - 24 q^{4} - 8 q^{5} + 4 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(119, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
119.2.g.a	$119$	$2$	119.g	17.c	$4$	$20$	$10$	$0.950$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{17}q^{3}+(-2+\beta _{12}+\beta _{13}+\cdots)q^{4}+\cdots\)