Space of modular forms of level 114, weight 3, and Character 114.g

• Label: 114.3.g
• Level: $114$
• Weight: $3$
• Character orbit: 114.g
• Rep. character: $\chi_{114}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	114.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(114, [\chi])\).

	Total	New	Old
Modular forms	88	24	64
Cusp forms	72	24	48
Eisenstein series	16	0	16

Trace form

\( 24 q - 2 q^{3} + 24 q^{4} + 4 q^{6} + 8 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(114, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
114.3.g.a	$114$	$3$	114.g	57.h	$6$	$24$	$12$	$3.106$		None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(114, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(114, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)