Space of modular forms of level 64, weight 6, and Character 64.b

• Label: 64.6.b
• Level: $64$
• Weight: $6$
• Character orbit: 64.b
• Rep. character: $\chi_{64}(33,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(64, [\chi])\).

	Total	New	Old
Modular forms	46	10	36
Cusp forms	34	10	24
Eisenstein series	12	0	12

Trace form

\( 10 q - 810 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(64, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.6.b.a	$64$	$6$	64.b	8.b	$2$	$2$	$2$	$10.265$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{3}+239q^{9}+237iq^{11}+1914q^{17}+\cdots\)
64.6.b.b	$64$	$6$	64.b	8.b	$2$	$8$	$8$	$10.265$	8.0.\(\cdots\).15	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{42}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+(-161+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(64, [\chi]) \cong \)