Space of modular forms of level 627, weight 2, and Character 627.be

• Label: 627.2.be
• Level: $627$
• Weight: $2$
• Character orbit: 627.be
• Rep. character: $\chi_{627}(10,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $160$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.be (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(160\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(627, [\chi])\).

	Total	New	Old
Modular forms	504	240	264
Cusp forms	456	240	216
Eisenstein series	48	0	48

Trace form

240 * q + 6 * q^11 - 48 * q^14 + 24 * q^15 - 216 * q^20 + 24 * q^26 - 36 * q^31 - 6 * q^33 - 132 * q^34 + 180 * q^38 + 12 * q^42 - 24 * q^44 - 12 * q^45 + 72 * q^47 + 48 * q^48 + 132 * q^49 + 108 * q^53 - 30 * q^55 - 24 * q^58 + 48 * q^60 - 120 * q^64 - 48 * q^66 + 48 * q^67 - 228 * q^70 - 84 * q^71 - 72 * q^77 + 84 * q^78 - 24 * q^80 - 156 * q^82 + 48 * q^86 + 108 * q^88 + 144 * q^89 - 24 * q^91 - 60 * q^92 - 24 * q^93 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(627, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
627.2.be.a	$627$	$2$	627.be	209.p	$18$	$240$	$40$	$5.007$		None		✓	✓	✓	627.2.be.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(627, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(627, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)