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

• Label: 819.2.de
• Level: $819$
• Weight: $2$
• Character orbit: 819.de
• Rep. character: $\chi_{819}(419,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Newform subspaces: $3$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.de (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 819 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

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

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

Trace form

\( 216 q - 6 q^{2} + 106 q^{4} + 2 q^{7} - 4 q^{9} + O(q^{10}) \)

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.de.a	$819$	$2$	819.de	819.ce	$6$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(-3\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
819.2.de.b	$819$	$2$	819.de	819.ce	$6$	$2$	$1$	$6.540$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(3\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
819.2.de.c	$819$	$2$	819.de	819.ce	$6$	$212$	$106$	$6.540$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$