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

• Label: 693.2.bg
• Level: $693$
• Weight: $2$
• Character orbit: 693.bg
• Rep. character: $\chi_{693}(10,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.bg (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	208	84	124
Cusp forms	176	76	100
Eisenstein series	32	8	24

Trace form

\( 76 q + 36 q^{4} + 12 q^{5} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
693.2.bg.a	$693$	$2$	693.bg	77.i	$6$	$12$	$6$	$5.534$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{7})q^{2}+(1-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
693.2.bg.b	$693$	$2$	693.bg	77.i	$6$	$32$	$16$	$5.534$		None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
693.2.bg.c	$693$	$2$	693.bg	77.i	$6$	$32$	$16$	$5.534$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(693, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)