Space of modular forms of level 806, weight 2, and Character 806.x

• Label: 806.2.x
• Level: $806$
• Weight: $2$
• Character orbit: 806.x
• Rep. character: $\chi_{806}(233,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $160$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 806 = 2 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	806.x (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 403 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(806, [\chi])\).

	Total	New	Old
Modular forms	464	160	304
Cusp forms	432	160	272
Eisenstein series	32	0	32

Trace form

\( 160 q + 4 q^{3} + 40 q^{4} - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(806, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
806.2.x.a	$806$	$2$	806.x	403.y	$10$	$160$	$40$	$6.436$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(806, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)