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

• Label: 768.2.ba
• Level: $768$
• Weight: $2$
• Character orbit: 768.ba
• Rep. character: $\chi_{768}(11,\cdot)$
• Character field: $\Q(\zeta_{64})$
• Dimension: $4032$
• 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.ba (of order \(64\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 768 \)
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	4160	0
Cusp forms	4032	4032	0
Eisenstein series	128	128	0

Trace form

4032 * q - 32 * q^3 - 64 * q^4 - 32 * q^6 - 64 * q^7 - 32 * q^9 - 64 * q^10 - 32 * q^12 - 64 * q^13 - 32 * q^15 - 64 * q^16 - 32 * q^18 - 64 * q^19 - 32 * q^21 - 64 * q^22 - 32 * q^24 - 64 * q^25 - 32 * q^27 - 64 * q^28 - 32 * q^30 - 64 * q^31 - 32 * q^33 - 64 * q^34 - 32 * q^36 - 64 * q^37 - 32 * q^39 - 64 * q^40 - 32 * q^42 - 64 * q^43 - 32 * q^45 - 64 * q^46 - 32 * q^48 - 64 * q^49 - 32 * q^51 - 64 * q^52 - 32 * q^54 - 64 * q^55 - 32 * q^57 - 64 * q^58 - 32 * q^60 - 64 * q^61 - 32 * q^63 - 64 * q^64 - 32 * q^66 - 64 * q^67 - 32 * q^69 - 64 * q^70 - 32 * q^72 - 64 * q^73 - 32 * q^75 - 64 * q^76 - 32 * q^78 - 64 * q^79 - 32 * q^81 - 64 * q^82 - 32 * q^84 - 64 * q^85 - 32 * q^87 - 64 * q^88 - 32 * q^90 - 64 * q^91 - 32 * q^93 - 64 * q^94 - 32 * q^96 - 64 * q^97 - 32 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
768.2.ba.a	$768$	$2$	768.ba	768.aa	$64$	$4032$	$126$	$6.133$		None		✓	✓	✓	768.2.ba.a	$4$	$0$	\(0\)	\(-32\)	\(0\)	\(-64\)		$\mathrm{SU}(2)[C_{64}]$