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

• Label: 114.3.c
• Level: $114$
• Weight: $3$
• Character orbit: 114.c
• Rep. character: $\chi_{114}(77,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
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	44	12	32
Cusp forms	36	12	24
Eisenstein series	8	0	8

Trace form

\( 12 q - 4 q^{3} - 24 q^{4} + 8 q^{6} - 8 q^{7} - 4 q^{9} + O(q^{10}) \)

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.c.a	$114$	$3$	114.c	3.b	$2$	$12$	$12$	$3.106$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{9}q^{3}-2q^{4}+\beta _{4}q^{5}+(1+\cdots)q^{6}+\cdots\)

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

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