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 + 4 * q^10 - 4 * q^11 + 12 * q^12 + 16 * q^16 - 12 * q^17 - 8 * q^18 + 20 * q^20 - 8 * q^21 - 20 * q^22 + 4 * q^24 + 8 * q^27 + 16 * q^29 - 36 * q^30 + 4 * q^31 - 16 * q^33 + 36 * q^34 + 16 * q^35 - 28 * q^37 + 48 * q^38 + 20 * q^39 - 24 * q^40 - 24 * q^41 - 28 * q^44 + 36 * q^45 + 8 * q^46 + 40 * q^47 - 8 * q^48 - 28 * q^50 - 40 * q^51 - 28 * q^54 - 40 * q^55 + 36 * q^57 + 56 * q^58 - 16 * q^61 - 40 * q^62 + 8 * q^63 + 32 * q^64 + 8 * q^65 - 32 * q^68 - 88 * q^69 - 8 * q^71 + 108 * q^72 + 8 * q^73 + 36 * q^74 + 8 * q^75 - 44 * q^78 - 4 * q^79 - 116 * q^80 + 4 * q^81 - 16 * q^82 - 32 * q^84 + 16 * q^85 + 44 * q^86 + 72 * q^88 + 48 * q^89 + 56 * q^90 + 20 * q^91 - 32 * q^92 + 44 * q^95 + 68 * q^96 - 24 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓	✓	✓	119.2.g.a	$2$	$0$	\(0\)	\(-4\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{17}q^{3}+(-2+\beta _{12}+\beta _{13}+\cdots)q^{4}+\cdots\)