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

• Label: 64.12.e
• Level: $64$
• Weight: $12$
• Character orbit: 64.e
• Rep. character: $\chi_{64}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $42$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	184	46	138
Cusp forms	168	42	126
Eisenstein series	16	4	12

Trace form

\( 42 q + 2 q^{3} - 2 q^{5} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.12.e.a	$64$	$12$	64.e	16.e	$4$	$42$	$21$	$49.174$		None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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