Space of modular forms of level 64, weight 4, and Character 64.b

• Label: 64.4.b
• Level: $64$
• Weight: $4$
• Character orbit: 64.b
• Rep. character: $\chi_{64}(33,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	64.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(64, [\chi])\).

	Total	New	Old
Modular forms	30	6	24
Cusp forms	18	6	12
Eisenstein series	12	0	12

Trace form

\( 6 q - 54 q^{9} + 156 q^{17} - 18 q^{25} - 696 q^{33} + 828 q^{41} + 1014 q^{49} - 1368 q^{57} - 2304 q^{65} + 876 q^{73} + 6942 q^{81} - 2676 q^{89} - 8772 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(64, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.4.b.a	$64$	$4$	64.b	8.b	$2$	$2$	$2$	$3.776$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)		✓			64.4.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+5\beta q^{3}-73 q^{9}+9\beta q^{11}+90 q^{17}+\cdots\)
64.4.b.b	$64$	$4$	64.b	8.b	$2$	$4$	$4$	$3.776$	\(\Q(\zeta_{12})\)	None		✓	✓		64.4.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{3}-\beta_{2} q^{5}+\beta_{3} q^{7}+23 q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

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