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

• Label: 693.2.k
• Level: $693$
• Weight: $2$
• Character orbit: 693.k
• Rep. character: $\chi_{693}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $160$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.k (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	200	160	40
Cusp forms	184	160	24
Eisenstein series	16	0	16

Trace form

\( 160 q - 80 q^{4} + 16 q^{5} - 8 q^{6} - 2 q^{7} + 4 q^{9} + O(q^{10}) \)

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.k.a	$693$	$2$	693.k	63.g	$3$	$6$	$3$	$5.534$	\(\Q(\zeta_{18})\)	None		✓			693.2.k.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
693.2.k.b	$693$	$2$	693.k	63.g	$3$	$74$	$37$	$5.534$		None		✓			693.2.k.b	$2$	$0$	\(0\)	\(0\)	\(14\)	\(-1\)		$\mathrm{SU}(2)[C_{3}]$
693.2.k.c	$693$	$2$	693.k	63.g	$3$	$80$	$40$	$5.534$		None		✓	✓		693.2.k.c	$2$	$0$	\(0\)	\(0\)	\(8\)	\(-1\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)