Space of modular forms of level 768, weight 2, and Character 768.z

• Label: 768.2.z
• Level: $768$
• Weight: $2$
• Character orbit: 768.z
• Rep. character: $\chi_{768}(13,\cdot)$
• Character field: $\Q(\zeta_{64})$
• Dimension: $2048$
• Newform subspaces: $1$
• Sturm bound: $256$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 256 \)
Character field:			\(\Q(\zeta_{64})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(256\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(768, [\chi])\).

	Total	New	Old
Modular forms	4160	2048	2112
Cusp forms	4032	2048	1984
Eisenstein series	128	0	128

Trace form

\( 2048 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(768, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
768.2.z.a	$768$	$2$	768.z	256.m	$64$	$2048$	$64$	$6.133$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{64}]$

Decomposition of \(S_{2}^{\mathrm{old}}(768, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)