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

• Label: 114.2.e
• Level: $114$
• Weight: $2$
• Character orbit: 114.e
• Rep. character: $\chi_{114}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	48	4	44
Cusp forms	32	4	28
Eisenstein series	16	0	16

Trace form

4 * q + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^7 - 2 * q^9 + 4 * q^10 - 4 * q^12 + 10 * q^13 + 4 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 8 * q^20 - 2 * q^21 - 4 * q^22 - 6 * q^25 - 8 * q^26 - 4 * q^27 + 2 * q^28 - 4 * q^29 + 8 * q^30 - 4 * q^31 + 4 * q^34 - 12 * q^35 - 2 * q^36 + 4 * q^37 + 8 * q^38 + 20 * q^39 + 4 * q^40 - 8 * q^41 - 4 * q^42 + 2 * q^43 - 8 * q^45 - 16 * q^46 - 12 * q^47 + 2 * q^48 - 8 * q^49 + 32 * q^50 + 4 * q^51 + 10 * q^52 + 8 * q^53 + 8 * q^55 - 8 * q^56 + 6 * q^57 + 8 * q^58 + 20 * q^59 - 4 * q^60 - 10 * q^61 - 4 * q^62 + 2 * q^63 + 4 * q^64 + 56 * q^65 + 4 * q^66 - 6 * q^67 + 8 * q^68 - 12 * q^70 - 16 * q^71 + 14 * q^73 - 12 * q^74 - 12 * q^75 + 6 * q^76 - 16 * q^77 - 4 * q^78 - 6 * q^79 + 4 * q^80 - 2 * q^81 - 8 * q^83 + 4 * q^84 - 16 * q^86 - 8 * q^87 + 8 * q^88 - 4 * q^89 + 4 * q^90 - 18 * q^91 - 2 * q^93 - 16 * q^94 - 4 * q^95 - 12 * q^97 - 8 * q^98

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.e.a	$114$	$2$	114.e	19.c	$3$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	None		✓			114.2.e.a	$2$	$0$	\(-1\)	\(1\)	\(4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.e.b	$114$	$2$	114.e	19.c	$3$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	None		✓			114.2.e.b	$2$	$0$	\(1\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)

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

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