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

• Label: 627.2.ba
• Level: $627$
• Weight: $2$
• Character orbit: 627.ba
• Rep. character: $\chi_{627}(89,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $396$
• 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.ba (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
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	396	108
Cusp forms	456	396	60
Eisenstein series	48	0	48

Trace form

396 * q + 12 * q^4 - 12 * q^10 - 6 * q^13 + 6 * q^15 - 60 * q^16 - 6 * q^19 + 42 * q^24 + 60 * q^28 - 42 * q^30 + 72 * q^34 - 60 * q^36 - 24 * q^39 + 24 * q^40 - 60 * q^42 - 66 * q^43 + 18 * q^45 - 84 * q^48 - 186 * q^49 + 36 * q^51 + 24 * q^52 + 72 * q^54 - 30 * q^57 - 72 * q^58 + 174 * q^60 + 24 * q^61 + 120 * q^63 - 240 * q^64 + 30 * q^66 - 30 * q^67 + 84 * q^70 - 90 * q^73 + 48 * q^76 - 54 * q^78 - 108 * q^79 - 72 * q^81 - 312 * q^82 - 216 * q^84 - 48 * q^85 + 12 * q^87 - 228 * q^90 - 96 * q^91 - 72 * q^93 + 204 * q^96 + 24 * q^97

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.ba.a	$627$	$2$	627.ba	57.j	$18$	$396$	$66$	$5.007$		None		✓	✓	✓	627.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

\( S_{2}^{\mathrm{old}}(627, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)