Space of modular forms of level 19, weight 12, and Character 19.e

• Label: 19.12.e
• Level: $19$
• Weight: $12$
• Character orbit: 19.e
• Rep. character: $\chi_{19}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $102$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 12 \)
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:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(19, [\chi])\).

	Total	New	Old
Modular forms	114	114	0
Cusp forms	102	102	0
Eisenstein series	12	12	0

Trace form

\( 102 q - 6 q^{2} - 795 q^{3} + 5928 q^{4} - 6 q^{5} - 14628 q^{6} - 57552 q^{7} - 294915 q^{8} + 466293 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(19, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.12.e.a	$19$	$12$	19.e	19.e	$9$	$102$	$17$	$14.599$		None		$2$	$0$	\(-6\)	\(-795\)	\(-6\)	\(-57552\)		$\mathrm{SU}(2)[C_{9}]$