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

• Label: 114.2.b
• Level: $114$
• Weight: $2$
• Character orbit: 114.b
• Rep. character: $\chi_{114}(113,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $40$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(40\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	24	8	16
Cusp forms	16	8	8
Eisenstein series	8	0	8

Trace form

8 * q + 8 * q^4 - 2 * q^6 - 12 * q^7 + 2 * q^9 + 8 * q^16 - 12 * q^19 - 2 * q^24 - 16 * q^25 - 12 * q^28 - 4 * q^30 + 2 * q^36 - 18 * q^39 - 22 * q^42 + 16 * q^43 + 52 * q^45 + 12 * q^49 - 20 * q^54 + 16 * q^55 + 18 * q^57 + 12 * q^58 - 24 * q^61 + 22 * q^63 + 8 * q^64 + 44 * q^66 + 28 * q^73 - 12 * q^76 - 46 * q^81 - 8 * q^85 - 78 * q^87 + 12 * q^93 - 2 * q^96 + 28 * 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.b.a	$114$	$2$	114.b	57.d	$2$	$2$	$2$	$0.910$	\(\Q(\sqrt{-2}) \)	None		✓			114.2.b.a	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
114.2.b.b	$114$	$2$	114.b	57.d	$2$	$2$	$2$	$0.910$	\(\Q(\sqrt{-3}) \)	None		✓			114.2.b.b	$2$	$0$	\(-2\)	\(3\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(2-4\zeta_{6})q^{5}+\cdots\)
114.2.b.c	$114$	$2$	114.b	57.d	$2$	$2$	$2$	$0.910$	\(\Q(\sqrt{-3}) \)	None		✓			114.2.b.b	$2$	$0$	\(2\)	\(-3\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(2-4\zeta_{6})q^{5}+\cdots\)
114.2.b.d	$114$	$2$	114.b	57.d	$2$	$2$	$2$	$0.910$	\(\Q(\sqrt{-2}) \)	None		✓			114.2.b.a	$2$	$0$	\(2\)	\(2\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots\)

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

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