Space of modular forms of level 16, weight 13, and Character 16.f

• Label: 16.13.f
• Level: $16$
• Weight: $13$
• Character orbit: 16.f
• Rep. character: $\chi_{16}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $46$
• Newform subspaces: $1$
• Sturm bound: $26$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(26\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(16, [\chi])\).

	Total	New	Old
Modular forms	50	50	0
Cusp forms	46	46	0
Eisenstein series	4	4	0

Trace form

\( 46 q - 2 q^{2} - 2 q^{3} - 4232 q^{4} - 2 q^{5} + 72928 q^{6} - 4 q^{7} - 478172 q^{8} + O(q^{10}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(16, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.13.f.a	$16$	$13$	16.f	16.f	$4$	$46$	$23$	$14.624$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$