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

• Label: 693.4.e
• Level: $693$
• Weight: $4$
• Character orbit: 693.e
• Rep. character: $\chi_{693}(188,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• 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.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
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	80	216
Cusp forms	280	80	200
Eisenstein series	16	0	16

Trace form

80 * q - 320 * q^4 + 64 * q^7 + 1280 * q^16 + 2000 * q^25 - 1600 * q^28 + 1568 * q^37 + 848 * q^43 + 1200 * q^46 + 368 * q^49 + 3240 * q^58 - 6056 * q^64 - 5456 * q^67 - 5616 * q^70 + 2464 * q^79 + 2688 * q^85 - 792 * q^88 + 1488 * q^91

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.e.a	$693$	$4$	693.e	21.c	$2$	$80$	$80$	$40.888$		None		✓	✓	✓	693.4.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(64\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)