Space of modular forms of level 64, weight 12, and Character 64.b

• Label: 64.12.b
• Level: $64$
• Weight: $12$
• Character orbit: 64.b
• Rep. character: $\chi_{64}(33,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 12 \)
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:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(64, [\chi])\).

	Total	New	Old
Modular forms	94	22	72
Cusp forms	82	22	60
Eisenstein series	12	0	12

Trace form

\( 22 q - 1299078 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.12.b.a	$64$	$12$	64.b	8.b	$2$	$2$	$2$	$49.174$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)		✓	64.12.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+197iq^{3}+21911q^{9}+70953iq^{11}+\cdots\)
64.12.b.b	$64$	$12$	64.b	8.b	$2$	$4$	$4$	$49.174$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		✓	64.12.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-15^{2}\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-25353q^{9}+\cdots\)
64.12.b.c	$64$	$12$	64.b	8.b	$2$	$16$	$16$	$49.174$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	64.12.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{178}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+(-77593+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)