Space of modular forms of level 669, weight 2, and Character 669.m

• Label: 669.2.m
• Level: $669$
• Weight: $2$
• Character orbit: 669.m
• Rep. character: $\chi_{669}(19,\cdot)$
• Character field: $\Q(\zeta_{111})$
• Dimension: $2664$
• Newform subspaces: $2$
• Sturm bound: $149$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.m (of order \(111\) and degree \(72\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 223 \)
Character field:			\(\Q(\zeta_{111})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(149\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(669, [\chi])\).

	Total	New	Old
Modular forms	5544	2664	2880
Cusp forms	5256	2664	2592
Eisenstein series	288	0	288

Trace form

2664 * q + q^3 - 72 * q^4 + 2 * q^6 + 6 * q^7 + 37 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 28 * q^13 + 16 * q^14 - 4 * q^15 - 68 * q^16 + 12 * q^17 - 2 * q^19 - 10 * q^20 - q^21 + 2 * q^22 + 8 * q^23 + 37 * q^25 - 4 * q^26 - 2 * q^27 - 20 * q^28 - 10 * q^29 + 24 * q^30 + 19 * q^31 + 40 * q^32 + 8 * q^33 - 8 * q^34 + 4 * q^35 + 36 * q^36 + 5 * q^37 - 20 * q^38 - 2 * q^39 - 450 * q^40 - 428 * q^41 + 16 * q^42 + 4 * q^43 - 26 * q^44 - 24 * q^46 + 16 * q^47 - 4 * q^48 + 8 * q^49 + 34 * q^50 - 150 * q^51 - 108 * q^52 + 26 * q^53 - 4 * q^54 - 12 * q^55 - 20 * q^56 + 8 * q^57 - 116 * q^58 - 20 * q^59 - 60 * q^60 - 10 * q^61 - 20 * q^62 - 3 * q^63 - 468 * q^64 + 16 * q^65 - 16 * q^66 - 5 * q^67 - 376 * q^68 + 4 * q^69 - 98 * q^70 - 10 * q^71 + q^73 + 2 * q^74 + 3 * q^75 + 16 * q^76 - 2 * q^77 - 2 * q^78 - 21 * q^79 - 10 * q^80 + 37 * q^81 - 56 * q^82 + 14 * q^84 - 132 * q^85 + 46 * q^86 - 8 * q^87 + 80 * q^88 - 12 * q^89 + 2 * q^90 + 20 * q^91 + 48 * q^92 - 15 * q^93 + 2 * q^94 - 212 * q^95 + 12 * q^96 - 32 * q^97 - 72 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(669, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
669.2.m.a	$669$	$2$	669.m	223.g	$111$	$1296$	$18$	$5.342$		None		✓			669.2.m.a	$2$	$0$	\(2\)	\(-18\)	\(-1\)	\(2\)		$\mathrm{SU}(2)[C_{111}]$
669.2.m.b	$669$	$2$	669.m	223.g	$111$	$1368$	$19$	$5.342$		None		✓	✓		669.2.m.b	$2$	$0$	\(-2\)	\(19\)	\(1\)	\(4\)		$\mathrm{SU}(2)[C_{111}]$

Decomposition of \(S_{2}^{\mathrm{old}}(669, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(669, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(223, [\chi])\)\(^{\oplus 2}\)