Space of modular forms of level 64, weight 2, and Character 64.b

• Label: 64.2.b
• Level: $64$
• Weight: $2$
• Character orbit: 64.b
• Rep. character: $\chi_{64}(33,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(64, [\chi])\).

	Total	New	Old
Modular forms	14	2	12
Cusp forms	2	2	0
Eisenstein series	12	0	12

Trace form

\( 2 q - 2 q^{9} - 12 q^{17} + 10 q^{25} + 24 q^{33} - 12 q^{41} - 14 q^{49} - 8 q^{57} + 4 q^{73} - 22 q^{81} + 36 q^{89} + 20 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(64, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.2.b.a	$64$	$2$	64.b	8.b	$2$	$2$	$2$	$0.511$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)		✓	✓	✓	64.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}-q^{9}-3\beta q^{11}-6 q^{17}+\beta q^{19}+\cdots\)