Space of modular forms of level 693, weight 2, and Character 693.ce

• Label: 693.2.ce
• Level: $693$
• Weight: $2$
• Character orbit: 693.ce
• Rep. character: $\chi_{693}(47,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $736$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.ce (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 693 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(693, [\chi])\).

	Total	New	Old
Modular forms	800	800	0
Cusp forms	736	736	0
Eisenstein series	64	64	0

Trace form

736 * q - 9 * q^2 - 9 * q^3 - 85 * q^4 - 18 * q^5 + 12 * q^6 - 3 * q^7 + 3 * q^9 - 48 * q^10 - 24 * q^12 - 9 * q^14 + 87 * q^16 + 13 * q^18 - 18 * q^19 - 18 * q^20 - 42 * q^21 - 12 * q^22 - 27 * q^24 - 158 * q^25 + 48 * q^26 + 27 * q^27 - 8 * q^28 - 18 * q^29 - 3 * q^30 - 9 * q^31 - 48 * q^32 - 84 * q^33 + 12 * q^34 + 75 * q^35 + 28 * q^36 - 6 * q^37 - 78 * q^38 + 15 * q^39 + 21 * q^42 - 16 * q^43 - 27 * q^44 - 24 * q^45 + 6 * q^46 - 9 * q^47 + 30 * q^48 - 3 * q^49 - 111 * q^50 - 41 * q^51 - 36 * q^53 - 108 * q^54 + 18 * q^56 - 34 * q^57 + 46 * q^58 + 21 * q^59 - 37 * q^60 - 9 * q^61 + 24 * q^62 - 53 * q^63 + 132 * q^64 - 12 * q^65 - 102 * q^66 + 8 * q^67 - 18 * q^68 + 27 * q^69 + 54 * q^70 - 35 * q^72 - 18 * q^73 + 51 * q^75 + 57 * q^77 + 16 * q^78 - 21 * q^79 - 24 * q^80 - 17 * q^81 - 30 * q^82 - 117 * q^84 - 28 * q^85 + 42 * q^87 - 32 * q^88 + 30 * q^89 + 12 * q^90 + 16 * q^91 - 168 * q^92 - 41 * q^93 - 9 * q^94 + 123 * q^95 + 63 * q^96 + 60 * q^98 - 112 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(693, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
693.2.ce.a	$693$	$2$	693.ce	693.be	$30$	$736$	$92$	$5.534$		None		✓	✓	✓	693.2.ce.a	$4$	$0$	\(-9\)	\(-9\)	\(-18\)	\(-3\)		$\mathrm{SU}(2)[C_{30}]$