Space of modular forms of level 696, weight 2, and Character 696.bs

• Label: 696.2.bs
• Level: $696$
• Weight: $2$
• Character orbit: 696.bs
• Rep. character: $\chi_{696}(77,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $1392$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	696.bs (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 696 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(696, [\chi])\).

	Total	New	Old
Modular forms	1488	1488	0
Cusp forms	1392	1392	0
Eisenstein series	96	96	0

Trace form

\( 1392 q - 28 q^{4} - 14 q^{6} - 40 q^{7} - 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(696, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
696.2.bs.a	$696$	$2$	696.bs	696.as	$28$	$24$	$2$	$5.558$		\(\Q(\sqrt{-6}) \)		✓			696.2.bs.a	$4$	$0$	\(-4\)	\(0\)	\(28\)	\(0\)		$\mathrm{U}(1)[D_{28}]$
696.2.bs.b	$696$	$2$	696.bs	696.as	$28$	$24$	$2$	$5.558$		\(\Q(\sqrt{-6}) \)		✓			696.2.bs.a	$4$	$0$	\(4\)	\(0\)	\(-28\)	\(0\)		$\mathrm{U}(1)[D_{28}]$
696.2.bs.c	$696$	$2$	696.bs	696.as	$28$	$1344$	$112$	$5.558$		None		✓	✓		696.2.bs.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)		$\mathrm{SU}(2)[C_{28}]$