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

• Label: 114.2.i
• Level: $114$
• Weight: $2$
• Character orbit: 114.i
• Rep. character: $\chi_{114}(25,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $40$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(40\)
Trace bound:			\(5\)
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	24	120
Cusp forms	96	24	72
Eisenstein series	48	0	48

Trace form

24 * q + 12 * q^7 + 12 * q^11 - 24 * q^14 - 24 * q^15 - 12 * q^17 - 24 * q^19 - 24 * q^20 - 24 * q^21 + 24 * q^22 + 12 * q^25 - 12 * q^26 - 12 * q^31 + 12 * q^33 + 12 * q^34 - 12 * q^35 + 12 * q^38 - 12 * q^41 + 12 * q^42 - 24 * q^43 + 12 * q^44 + 12 * q^45 + 12 * q^46 + 12 * q^47 - 24 * q^49 + 48 * q^53 + 24 * q^56 + 12 * q^57 - 24 * q^58 + 36 * q^59 + 12 * q^60 - 24 * q^61 + 36 * q^62 - 12 * q^64 - 12 * q^65 + 12 * q^68 + 24 * q^69 + 24 * q^70 + 60 * q^71 + 48 * q^73 + 36 * q^74 + 12 * q^76 + 24 * q^77 + 24 * q^78 - 24 * q^79 - 36 * q^82 - 36 * q^83 + 12 * q^84 - 24 * q^85 - 24 * q^86 - 12 * q^87 + 12 * q^88 - 36 * q^89 - 36 * q^91 - 36 * q^92 + 36 * q^93 - 72 * q^94 + 12 * q^95 - 24 * q^97 - 72 * q^98 + 12 * 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.i.a	$114$	$2$	114.i	19.e	$9$	$6$	$1$	$0.910$	\(\Q(\zeta_{18})\)	None		✓			114.2.i.a	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
114.2.i.b	$114$	$2$	114.i	19.e	$9$	$6$	$1$	$0.910$	\(\Q(\zeta_{18})\)	None		✓			114.2.i.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
114.2.i.c	$114$	$2$	114.i	19.e	$9$	$6$	$1$	$0.910$	\(\Q(\zeta_{18})\)	None		✓			114.2.i.c	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
114.2.i.d	$114$	$2$	114.i	19.e	$9$	$6$	$1$	$0.910$	\(\Q(\zeta_{18})\)	None		✓			114.2.i.d	$2$	$0$	\(0\)	\(0\)	\(9\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(114, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)