Space of modular forms of level 64, weight 13, and Character 64.f

• Label: 64.13.f
• Level: $64$
• Weight: $13$
• Character orbit: 64.f
• Rep. character: $\chi_{64}(15,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $46$
• Newform subspaces: $1$
• Sturm bound: $104$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	64.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(104\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(64, [\chi])\).

	Total	New	Old
Modular forms	200	50	150
Cusp forms	184	46	138
Eisenstein series	16	4	12

Trace form

\( 46 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.13.f.a	$64$	$13$	64.f	16.f	$4$	$46$	$23$	$58.496$		None			16.13.f.a	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{13}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{13}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{13}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)