Space of modular forms of level 765, weight 2, and Character 765.cr

• Label: 765.2.cr
• Level: $765$
• Weight: $2$
• Character orbit: 765.cr
• Rep. character: $\chi_{765}(14,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $1664$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.cr (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 765 \)
Character field:			\(\Q(\zeta_{48})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(765, [\chi])\).

	Total	New	Old
Modular forms	1792	1792	0
Cusp forms	1664	1664	0
Eisenstein series	128	128	0

Trace form

1664 * q - 16 * q^4 - 24 * q^5 - 32 * q^6 - 32 * q^9 - 32 * q^10 - 48 * q^11 - 48 * q^14 - 40 * q^15 - 64 * q^19 - 24 * q^20 - 128 * q^21 - 32 * q^24 - 8 * q^25 - 48 * q^29 - 16 * q^30 - 16 * q^31 + 32 * q^34 - 48 * q^39 - 8 * q^40 - 48 * q^41 - 16 * q^45 - 64 * q^46 - 16 * q^49 - 32 * q^51 - 128 * q^54 - 32 * q^55 - 48 * q^56 - 48 * q^59 - 224 * q^60 - 16 * q^61 - 192 * q^64 - 24 * q^65 - 64 * q^66 - 64 * q^69 - 24 * q^70 - 48 * q^74 + 80 * q^75 - 16 * q^76 - 16 * q^79 - 32 * q^81 - 8 * q^85 - 576 * q^86 + 144 * q^90 - 160 * q^91 - 16 * q^94 + 216 * q^95 - 432 * q^96 - 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(765, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
765.2.cr.a	$765$	$2$	765.cr	765.br	$48$	$1664$	$104$	$6.109$		None		✓	✓	✓	765.2.cr.a	$8$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{48}]$