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

• Label: 114.2.h
• Level: $114$
• Weight: $2$
• Character orbit: 114.h
• Rep. character: $\chi_{114}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $6$
• Sturm bound: $40$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(40\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

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

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

Trace form

16 * q - 3 * q^3 - 8 * q^4 - q^6 + 12 * q^7 + q^9 - 18 * q^13 + 6 * q^15 - 8 * q^16 - 18 * q^19 - 6 * q^22 - q^24 + 16 * q^25 - 6 * q^28 + 4 * q^30 - 3 * q^33 + 12 * q^34 + q^36 - 48 * q^39 + 22 * q^42 + 2 * q^43 - 52 * q^45 + 3 * q^48 - 12 * q^49 + 72 * q^51 + 18 * q^52 + 20 * q^54 - 4 * q^55 + 48 * q^57 - 6 * q^60 - 18 * q^61 - 16 * q^63 + 16 * q^64 + 25 * q^66 + 36 * q^67 - 12 * q^70 + 3 * q^72 + 8 * q^73 + 12 * q^76 + 6 * q^78 - 30 * q^79 - 23 * q^81 - 6 * q^82 + 8 * q^85 - 12 * q^87 - 78 * q^90 - 6 * q^91 - 6 * q^93 + 2 * q^96 + 18 * q^97 + 23 * 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.h.a	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	None		✓			114.2.h.a	$2$	$1$	\(-1\)	\(-3\)	\(-6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.b	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	None		✓			114.2.h.b	$2$	$0$	\(-1\)	\(-3\)	\(6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.c	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	None		✓			114.2.h.b	$2$	$0$	\(1\)	\(-3\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.d	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	None		✓			114.2.h.a	$2$	$0$	\(1\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.e	$114$	$2$	114.h	57.f	$6$	$4$	$2$	$0.910$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			114.2.h.e	$2$	$0$	\(-2\)	\(4\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
114.2.h.f	$114$	$2$	114.h	57.f	$6$	$4$	$2$	$0.910$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			114.2.h.e	$2$	$0$	\(2\)	\(2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)

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

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