Space of modular forms of level 3, weight 19, and Character 3.b

• Label: 3.19.b
• Level: $3$
• Weight: $19$
• Character orbit: 3.b
• Rep. character: $\chi_{3}(2,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $6$
• Trace bound: $1$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(3, [\chi])\).

	Total	New	Old
Modular forms	7	7	0
Cusp forms	5	5	0
Eisenstein series	2	2	0

Trace form

\( 5 q - 3807 q^{3} - 791392 q^{4} + 22698144 q^{6} - 18194966 q^{7} - 497920851 q^{9} + O(q^{10}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(3, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.19.b.a	$3$	$19$	3.b	3.b	$2$	$1$	$1$	$6.162$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-19683\)	\(0\)	\(77549186\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{9}q^{3}+2^{18}q^{4}+77549186q^{7}+\cdots\)
3.19.b.b	$3$	$19$	3.b	3.b	$2$	$4$	$4$	$6.162$	4.0.601940665.1	None		$2$	$0$	\(0\)	\(15876\)	\(0\)	\(-95744152\)	$2^{11}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots\)