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

• Label: 819.2.em
• Level: $819$
• Weight: $2$
• Character orbit: 819.em
• Rep. character: $\chi_{819}(158,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $432$
• 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.em (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 819 \)
Character field:			\(\Q(\zeta_{12})\)
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	464	464	0
Cusp forms	432	432	0
Eisenstein series	32	32	0

Trace form

\( 432 q - 6 q^{2} - 4 q^{3} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9} + O(q^{10}) \)

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.em.a	$819$	$2$	819.em	819.dm	$12$	$432$	$108$	$6.540$		None		$2$	$0$	\(-6\)	\(-4\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{12}]$