Space of modular forms of level 19, weight 10, and Character 19.c

• Label: 19.10.c
• Level: $19$
• Weight: $10$
• Character orbit: 19.c
• Rep. character: $\chi_{19}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(19, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	28	28	0
Eisenstein series	4	4	0

Trace form

\( 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(19, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.10.c.a	$19$	$10$	19.c	19.c	$3$	$28$	$14$	$9.786$		None		$2$	$0$	\(15\)	\(-74\)	\(-285\)	\(-2676\)		$\mathrm{SU}(2)[C_{3}]$