Space of modular forms of level 847, weight 2, and Character 847.ba

• Label: 847.2.ba
• Level: $847$
• Weight: $2$
• Character orbit: 847.ba
• Rep. character: $\chi_{847}(6,\cdot)$
• Character field: $\Q(\zeta_{110})$
• Dimension: $3440$
• Newform subspaces: $2$
• Sturm bound: $176$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.ba (of order \(110\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 847 \)
Character field:			\(\Q(\zeta_{110})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(176\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(847, [\chi])\).

	Total	New	Old
Modular forms	3600	3600	0
Cusp forms	3440	3440	0
Eisenstein series	160	160	0

Trace form

\( 3440 q - 78 q^{2} - 168 q^{4} - 34 q^{7} - 88 q^{8} + 754 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(847, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
847.2.ba.a	$847$	$2$	847.ba	847.aa	$110$	$80$	$2$	$6.763$		\(\Q(\sqrt{-7}) \)		✓			847.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{110}]$
847.2.ba.b	$847$	$2$	847.ba	847.aa	$110$	$3360$	$84$	$6.763$		None		✓	✓		847.2.ba.b	$4$	$0$	\(-78\)	\(0\)	\(0\)	\(-34\)		$\mathrm{SU}(2)[C_{110}]$