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

• Label: 819.2.r
• Level: $819$
• Weight: $2$
• Character orbit: 819.r
• Rep. character: $\chi_{819}(625,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $192$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.r (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	232	192	40
Cusp forms	216	192	24
Eisenstein series	16	0	16

Trace form

\( 192 q + 192 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
819.2.r.a	$819$	$2$	819.r	63.h	$3$	$96$	$48$	$6.540$		None		$2$	$0$	\(-12\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$
819.2.r.b	$819$	$2$	819.r	63.h	$3$	$96$	$48$	$6.540$		None		$2$	$0$	\(12\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \)