Space of modular forms of level 19, weight 2, and Character 19.e

• Label: 19.2.e
• Level: $19$
• Weight: $2$
• Character orbit: 19.e
• Rep. character: $\chi_{19}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	19.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(19, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	6	6	0
Eisenstein series	12	12	0

Trace form

\( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(19, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.2.e.a	$19$	$2$	19.e	19.e	$9$	$6$	$1$	$0.152$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(-6\)	\(-3\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)