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

• Label: 19.3.b
• Level: $19$
• Weight: $3$
• Character orbit: 19.b
• Rep. character: $\chi_{19}(18,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $5$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	19.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(5\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	5	5	0
Cusp forms	3	3	0
Eisenstein series	2	2	0

Trace form

\( 3 q - 14 q^{4} - q^{5} + 26 q^{6} - 15 q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(19, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.3.b.a	$19$	$3$	19.b	19.b	$2$	$1$	$1$	$0.518$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots\)
19.3.b.b	$19$	$3$	19.b	19.b	$2$	$2$	$2$	$0.518$	\(\Q(\sqrt{-13}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots\)