Space of modular forms of level 19, weight 6, and Character 19.e

• Label: 19.6.e
• Level: $19$
• Weight: $6$
• Character orbit: 19.e
• Rep. character: $\chi_{19}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $42$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(19, [\chi])\).

	Total	New	Old
Modular forms	54	54	0
Cusp forms	42	42	0
Eisenstein series	12	12	0

Trace form

\( 42 q - 6 q^{2} - 39 q^{3} + 24 q^{4} - 6 q^{5} - 264 q^{6} - 180 q^{7} + 573 q^{8} - 105 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(19, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.6.e.a	$19$	$6$	19.e	19.e	$9$	$42$	$7$	$3.047$		None		$2$	$0$	\(-6\)	\(-39\)	\(-6\)	\(-180\)		$\mathrm{SU}(2)[C_{9}]$