Space of modular forms of level 693, weight 4, and Character 693.g

• Label: 693.4.g
• Level: $693$
• Weight: $4$
• Character orbit: 693.g
• Rep. character: $\chi_{693}(197,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $384$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	693.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(693, [\chi])\).

	Total	New	Old
Modular forms	296	72	224
Cusp forms	280	72	208
Eisenstein series	16	0	16

Trace form

72 * q + 288 * q^4 + 1320 * q^16 - 588 * q^22 - 2328 * q^25 - 384 * q^31 + 576 * q^34 - 240 * q^37 - 3528 * q^49 - 3456 * q^55 + 4560 * q^58 + 5016 * q^64 + 48 * q^67 + 1512 * q^70 - 11760 * q^82 - 6900 * q^88 - 768 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(693, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
693.4.g.a	$693$	$4$	693.g	33.d	$2$	$72$	$72$	$40.888$		None		✓	✓	✓	693.4.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)