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

• Label: 693.2.bs
• Level: $693$
• Weight: $2$
• Character orbit: 693.bs
• Rep. character: $\chi_{693}(125,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $128$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.bs (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 231 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
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	416	128	288
Cusp forms	352	128	224
Eisenstein series	64	0	64

Trace form

\( 128 q + 32 q^{4} - 8 q^{7} + O(q^{10}) \)

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.bs.a	$693$	$2$	693.bs	231.u	$10$	$32$	$8$	$5.534$		\(\Q(\sqrt{-7}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{10}]$
693.2.bs.b	$693$	$2$	693.bs	231.u	$10$	$96$	$24$	$5.534$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{10}]$

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

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