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 - 24 * q^13 - 6 * q^15 - 12 * q^19 - 48 * q^22 + 3 * q^24 - 36 * q^25 - 9 * q^27 + 12 * q^28 - 51 * q^33 - 12 * q^34 - 3 * q^36 + 12 * q^39 - 12 * q^43 + 36 * q^46 + 6 * q^48 + 42 * q^49 + 9 * q^51 - 12 * q^52 + 54 * q^54 + 60 * q^55 + 24 * q^57 + 24 * q^58 + 42 * q^60 + 108 * q^61 + 66 * q^63 - 18 * q^64 + 3 * q^66 - 30 * q^67 + 54 * q^69 + 48 * q^70 + 6 * q^72 - 84 * q^73 - 42 * q^78 - 12 * q^79 - 3 * q^81 + 6 * q^82 - 54 * q^84 - 54 * q^87 - 12 * q^90 - 36 * q^91 - 150 * q^93 + 18 * q^97 - 132 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
114.2.l.a	$114$	$2$	114.l	57.j	$18$	$18$	$3$	$0.910$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			114.2.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(-\beta _{6}-\beta _{7})q^{2}+(\beta _{1}-\beta _{17})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
114.2.l.b	$114$	$2$	114.l	57.j	$18$	$18$	$3$	$0.910$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			114.2.l.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q-\beta _{4}q^{2}+\beta _{5}q^{3}-\beta _{7}q^{4}+(\beta _{9}-\beta _{17})q^{5}+\cdots\)

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

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