Space of modular forms of level 114, weight 2, and Character 114.l

• Label: 114.2.l
• Level: $114$
• Weight: $2$
• Character orbit: 114.l
• Rep. character: $\chi_{114}(29,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(40\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(114, [\chi])\).

	Total	New	Old
Modular forms	144	36	108
Cusp forms	96	36	60
Eisenstein series	48	0	48

Trace form

\( 36 q + 3 q^{3} + 3 q^{6} - 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(114, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
114.2.l.a	$114$	$2$	114.l	57.j	$18$	$18$	$3$	$0.910$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(-\beta _{6}-\beta _{7})q^{2}+(\beta _{1}-\beta _{17})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
114.2.l.b	$114$	$2$	114.l	57.j	$18$	$18$	$3$	$0.910$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q-\beta _{4}q^{2}+\beta _{5}q^{3}-\beta _{7}q^{4}+(\beta _{9}-\beta _{17})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(114, [\chi])\) into lower level spaces

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