Space of modular forms of level 19, weight 5, and Character 19.f

• Label: 19.5.f
• Level: $19$
• Weight: $5$
• Character orbit: 19.f
• Rep. character: $\chi_{19}(2,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(19, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	36	36	0
Eisenstein series	12	12	0

Trace form

\( 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(19, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.5.f.a	$19$	$5$	19.f	19.f	$18$	$36$	$6$	$1.964$		None		$2$	$0$	\(-6\)	\(-18\)	\(-6\)	\(-48\)		$\mathrm{SU}(2)[C_{18}]$