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

• Label: 669.2.e
• Level: $669$
• Weight: $2$
• Character orbit: 669.e
• Rep. character: $\chi_{669}(262,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $74$
• Newform subspaces: $4$
• Sturm bound: $149$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 223 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
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	154	74	80
Cusp forms	146	74	72
Eisenstein series	8	0	8

Trace form

74 * 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 + 6 * q^40 - 16 * 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 + 2 * q^51 + 108 * q^52 - 26 * q^53 + 4 * q^54 + 12 * q^55 + 20 * q^56 - 8 * q^57 - 32 * q^58 + 20 * q^59 + 60 * q^60 + 10 * q^61 + 20 * q^62 + 3 * q^63 + 24 * q^64 - 16 * q^65 + 16 * q^66 + 5 * q^67 - 68 * q^68 - 4 * q^69 - 50 * 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 - 16 * 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.e.a	$669$	$2$	669.e	223.c	$3$	$2$	$1$	$5.342$	\(\Q(\sqrt{-3}) \)	None		✓			669.2.e.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2q^{4}+3q^{7}-\zeta_{6}q^{9}+\cdots\)
669.2.e.b	$669$	$2$	669.e	223.c	$3$	$4$	$2$	$5.342$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		✓			669.2.e.b	$2$	$0$	\(4\)	\(2\)	\(-3\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1+\beta _{1})q^{3}-q^{4}+(2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
669.2.e.c	$669$	$2$	669.e	223.c	$3$	$30$	$15$	$5.342$		None		✓			669.2.e.c	$2$	$0$	\(-6\)	\(15\)	\(4\)	\(-6\)		$\mathrm{SU}(2)[C_{3}]$
669.2.e.d	$669$	$2$	669.e	223.c	$3$	$38$	$19$	$5.342$		None		✓	✓		669.2.e.d	$2$	$0$	\(2\)	\(-19\)	\(-1\)	\(-4\)		$\mathrm{SU}(2)[C_{3}]$

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

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