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

• Label: 847.2.p
• Level: $847$
• Weight: $2$
• Character orbit: 847.p
• Rep. character: $\chi_{847}(76,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $860$
• 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.p (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 847 \)
Character field:			\(\Q(\zeta_{22})\)
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	900	900	0
Cusp forms	860	860	0
Eisenstein series	40	40	0

Trace form

\( 860 q - 22 q^{2} + 68 q^{4} - 11 q^{7} - 22 q^{8} - 864 q^{9} + O(q^{10}) \)

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	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
847.2.p.a	$847$	$2$	847.p	847.p	$22$	$20$	$2$	$6.763$	20.0.\(\cdots\).2	\(\Q(\sqrt{-7}) \)		✓	847.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{22}]$	\(q+(\beta _{2}-\beta _{10}+\beta _{19})q^{2}+(-\beta _{5}-2\beta _{8}+\cdots)q^{4}+\cdots\)
847.2.p.b	$847$	$2$	847.p	847.p	$22$	$840$	$84$	$6.763$		None		✓	847.2.p.b	$4$	$0$	\(-22\)	\(0\)	\(0\)	\(-11\)		$\mathrm{SU}(2)[C_{22}]$