Space of modular forms of level 819, weight 2, and Character 819.bh

• Label: 819.2.bh
• Level: $819$
• Weight: $2$
• Character orbit: 819.bh
• Rep. character: $\chi_{819}(589,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $168$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bh (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

	Total	New	Old
Modular forms	232	168	64
Cusp forms	216	168	48
Eisenstein series	16	0	16

Trace form

\( 168 q - 168 q^{4} + 18 q^{6} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
819.2.bh.a	$819$	$2$	819.bh	117.l	$6$	$168$	$84$	$6.540$		None		✓	✓	✓	819.2.bh.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(819, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)