Space of modular forms of level 13, weight 8, and Character 13.c

• Label: 13.8.c
• Level: $13$
• Weight: $8$
• Character orbit: 13.c
• Rep. character: $\chi_{13}(3,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	13.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(13, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

Trace form

\( 16 q - 9 q^{2} - 28 q^{3} - 577 q^{4} + 384 q^{5} + 342 q^{6} + 196 q^{7} + 5922 q^{8} - 5988 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(13, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
13.8.c.a	$13$	$8$	13.c	13.c	$3$	$16$	$8$	$4.061$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-9\)	\(-28\)	\(384\)	\(196\)	$2^{12}\cdot 3\cdot 13^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{2})q^{2}+(-4-4\beta _{2}+\cdots)q^{3}+\cdots\)