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

• Label: 19.7.d
• Level: $19$
• Weight: $7$
• Character orbit: 19.d
• Rep. character: $\chi_{19}(8,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $11$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(11\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

\( 18 q - 3 q^{2} + 27 q^{3} + 189 q^{4} - 57 q^{5} - 371 q^{6} - 260 q^{7} + 2390 q^{9} + O(q^{10}) \)

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.d.a	$19$	$7$	19.d	19.d	$6$	$18$	$9$	$4.371$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-3\)	\(27\)	\(-57\)	\(-260\)	$2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 19^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(2+\beta _{2}-\beta _{7})q^{3}+(21+\cdots)q^{4}+\cdots\)