Space of modular forms of level 19, weight 7, and Character 19.b

• Label: 19.7.b
• Level: $19$
• Weight: $7$
• Character orbit: 19.b
• Rep. character: $\chi_{19}(18,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $2$
• Sturm bound: $11$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(11\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(19, [\chi])\).

	Total	New	Old
Modular forms	11	11	0
Cusp forms	9	9	0
Eisenstein series	2	2	0

Trace form

\( 9 q - 390 q^{4} + 54 q^{5} - 358 q^{6} + 470 q^{7} - 323 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(19, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.7.b.a	$19$	$7$	19.b	19.b	$2$	$1$	$1$	$4.371$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-54\)	\(610\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{6}q^{4}-54q^{5}+610q^{7}+3^{6}q^{9}+\cdots\)
19.7.b.b	$19$	$7$	19.b	19.b	$2$	$8$	$8$	$4.371$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(108\)	\(-140\)	$2^{3}\cdot 29$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-57+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)