Space of modular forms of level 614, weight 2, and Character 614.c

• Label: 614.2.c
• Level: $614$
• Weight: $2$
• Character orbit: 614.c
• Rep. character: $\chi_{614}(17,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $54$
• Newform subspaces: $4$
• Sturm bound: $154$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 614 = 2 \cdot 307 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	614.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 307 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(154\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(614, [\chi])\).

	Total	New	Old
Modular forms	158	54	104
Cusp forms	150	54	96
Eisenstein series	8	0	8

Trace form

54 * q + 2 * q^2 + 2 * q^3 + 54 * q^4 - 2 * q^5 - 6 * q^6 - 8 * q^7 + 2 * q^8 + 48 * q^9 - 5 * q^11 + 2 * q^12 - 4 * q^13 + 18 * q^15 + 54 * q^16 - 26 * q^17 - 4 * q^18 - 4 * q^19 - 2 * q^20 - 8 * q^21 - 11 * q^22 - 4 * q^23 - 6 * q^24 - 23 * q^25 - 4 * q^26 + 2 * q^27 - 8 * q^28 - 4 * q^29 - 6 * q^30 + 14 * q^31 + 2 * q^32 - 11 * q^33 - 14 * q^34 + 68 * q^35 + 48 * q^36 + 4 * q^37 - 12 * q^38 - 18 * q^39 + q^41 - 20 * q^42 + 15 * q^43 - 5 * q^44 - 48 * q^45 + 2 * q^46 + 2 * q^47 + 2 * q^48 - 43 * q^49 - 23 * q^50 - 10 * q^51 - 4 * q^52 + 10 * q^53 + 30 * q^54 + 14 * q^55 + 44 * q^57 + 10 * q^58 + 15 * q^59 + 18 * q^60 + 10 * q^61 - 10 * q^62 - 48 * q^63 + 54 * q^64 + 18 * q^65 + 13 * q^66 + 25 * q^67 - 26 * q^68 + 6 * q^69 - 16 * q^70 - 4 * q^72 + 13 * q^73 + 27 * q^75 - 4 * q^76 - 40 * q^77 - 26 * q^78 - 32 * q^79 - 2 * q^80 + 54 * q^81 - 9 * q^82 - 14 * q^83 - 8 * q^84 - 8 * q^85 - 5 * q^86 + 4 * q^87 - 11 * q^88 - 24 * q^89 + 10 * q^90 + 76 * q^91 - 4 * q^92 + 20 * q^93 - 10 * q^94 + 8 * q^95 - 6 * q^96 - 74 * q^97 - 9 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(614, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
614.2.c.a	$614$	$2$	614.c	307.c	$3$	$2$	$1$	$4.903$	\(\Q(\sqrt{-3}) \)	None		✓			614.2.c.a	$2$	$1$	\(2\)	\(-6\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}-3q^{3}+q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
614.2.c.b	$614$	$2$	614.c	307.c	$3$	$4$	$2$	$4.903$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			614.2.c.b	$2$	$0$	\(4\)	\(8\)	\(2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+2q^{3}+q^{4}+\beta _{1}q^{5}+2q^{6}+\cdots\)
614.2.c.c	$614$	$2$	614.c	307.c	$3$	$22$	$11$	$4.903$		None		✓			614.2.c.c	$2$	$0$	\(22\)	\(-4\)	\(1\)	\(-2\)		$\mathrm{SU}(2)[C_{3}]$
614.2.c.d	$614$	$2$	614.c	307.c	$3$	$26$	$13$	$4.903$		None		✓	✓		614.2.c.d	$2$	$0$	\(-26\)	\(4\)	\(-1\)	\(-4\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(614, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(614, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(307, [\chi])\)\(^{\oplus 2}\)