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

• Label: 627.2.r
• Level: $627$
• Weight: $2$
• Character orbit: 627.r
• Rep. character: $\chi_{627}(100,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $204$
• Newform subspaces: $4$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.r (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	504	204	300
Cusp forms	456	204	252
Eisenstein series	48	0	48

Trace form

204 * q + 12 * q^4 + 12 * q^6 + 48 * q^10 + 12 * q^12 + 18 * q^13 + 36 * q^14 - 36 * q^16 - 24 * q^17 - 18 * q^19 - 6 * q^21 - 48 * q^24 + 24 * q^25 + 6 * q^27 - 60 * q^28 + 24 * q^29 + 60 * q^31 - 48 * q^32 + 24 * q^34 - 72 * q^35 + 12 * q^36 - 24 * q^37 + 108 * q^38 + 96 * q^40 - 48 * q^41 + 12 * q^42 - 78 * q^43 - 60 * q^46 + 60 * q^47 - 114 * q^49 - 36 * q^50 + 24 * q^51 - 72 * q^52 + 12 * q^54 + 72 * q^58 + 60 * q^59 - 24 * q^60 - 24 * q^61 + 84 * q^62 - 12 * q^63 - 84 * q^64 - 18 * q^67 - 12 * q^68 + 132 * q^70 - 84 * q^71 - 72 * q^72 + 66 * q^73 - 144 * q^74 - 84 * q^75 + 48 * q^76 + 84 * q^78 - 72 * q^79 - 276 * q^80 + 72 * q^82 - 48 * q^83 - 48 * q^85 - 168 * q^86 + 36 * q^88 - 24 * q^89 + 12 * q^90 - 96 * q^91 - 84 * q^92 - 24 * q^93 - 48 * q^94 - 36 * q^95 + 48 * q^96 - 60 * q^97 + 192 * q^98

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.r.a	$627$	$2$	627.r	19.e	$9$	$42$	$7$	$5.007$		None		✓			627.2.r.a	$2$	$0$	\(3\)	\(0\)	\(0\)	\(18\)		$\mathrm{SU}(2)[C_{9}]$
627.2.r.b	$627$	$2$	627.r	19.e	$9$	$48$	$8$	$5.007$		None		✓			627.2.r.b	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(18\)		$\mathrm{SU}(2)[C_{9}]$
627.2.r.c	$627$	$2$	627.r	19.e	$9$	$54$	$9$	$5.007$		None		✓			627.2.r.c	$2$	$0$	\(3\)	\(0\)	\(0\)	\(-18\)		$\mathrm{SU}(2)[C_{9}]$
627.2.r.d	$627$	$2$	627.r	19.e	$9$	$60$	$10$	$5.007$		None		✓	✓		627.2.r.d	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-18\)		$\mathrm{SU}(2)[C_{9}]$

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

\( S_{2}^{\mathrm{old}}(627, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)