Space of modular forms of level 819, weight 1, and Character 819.ek

• Label: 819.1.ek
• Level: $819$
• Weight: $1$
• Character orbit: 819.ek
• Rep. character: $\chi_{819}(139,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	819.ek (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 819 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(819, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	4	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
819.1.ek.a	$819$	$1$	819.ek	819.dk	$6$	$4$	$2$	$0.409$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}q^{6}+\cdots\)