Space of modular forms of level 64, weight 8, and Character 64.b

• Label: 64.8.b
• Level: $64$
• Weight: $8$
• Character orbit: 64.b
• Rep. character: $\chi_{64}(33,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $3$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(64, [\chi])\).

	Total	New	Old
Modular forms	62	14	48
Cusp forms	50	14	36
Eisenstein series	12	0	12

Trace form

\( 14 q - 10206 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(64, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.8.b.a	$64$	$8$	64.b	8.b	$2$	$2$	$2$	$19.993$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+43iq^{3}-5209q^{9}+4407iq^{11}+\cdots\)
64.8.b.b	$64$	$8$	64.b	8.b	$2$	$4$	$4$	$19.993$	\(\Q(i, \sqrt{435})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+15\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}+1287q^{9}+\cdots\)
64.8.b.c	$64$	$8$	64.b	8.b	$2$	$8$	$8$	$19.993$	8.0.\(\cdots\).10	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{42}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}+\beta _{6})q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+(-617+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(64, [\chi]) \cong \)