Space of modular forms of level 64, weight 3, and Character 64.d

• Label: 64.3.d
• Level: $64$
• Weight: $3$
• Character orbit: 64.d
• Rep. character: $\chi_{64}(31,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	64.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(64, [\chi])\).

	Total	New	Old
Modular forms	22	4	18
Cusp forms	10	4	6
Eisenstein series	12	0	12

Trace form

\( 4 q + 12 q^{9} - 24 q^{17} - 92 q^{25} + 48 q^{33} + 264 q^{41} - 60 q^{49} - 336 q^{57} + 192 q^{65} + 232 q^{73} - 396 q^{81} - 408 q^{89} + 104 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.3.d.a	$64$	$3$	64.d	8.d	$2$	$4$	$4$	$1.744$	\(\Q(\zeta_{12})\)	None		✓	✓	✓	64.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{3}-\beta_{2} q^{5}-\beta_{3} q^{7}+3 q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)