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

• Label: 765.2.bx
• Level: $765$
• Weight: $2$
• Character orbit: 765.bx
• Rep. character: $\chi_{765}(73,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $344$
• Newform subspaces: $3$
• Sturm bound: $216$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.bx (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(216\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	928	376	552
Cusp forms	800	344	456
Eisenstein series	128	32	96

Trace form

344 * q + 8 * q^2 + 8 * q^5 - 8 * q^7 - 8 * q^8 - 8 * q^10 + 16 * q^11 + 32 * q^14 + 8 * q^17 + 32 * q^19 + 48 * q^20 - 8 * q^22 + 8 * q^23 + 48 * q^26 - 8 * q^28 - 48 * q^31 + 24 * q^32 - 32 * q^34 + 16 * q^35 + 24 * q^37 + 16 * q^38 + 48 * q^40 + 56 * q^41 - 8 * q^43 - 32 * q^46 - 64 * q^47 - 32 * q^50 - 80 * q^52 + 56 * q^53 - 40 * q^55 + 16 * q^56 + 48 * q^58 + 112 * q^59 - 16 * q^61 - 40 * q^62 + 32 * q^64 - 32 * q^65 - 64 * q^67 - 8 * q^68 + 88 * q^70 + 8 * q^73 + 40 * q^74 + 48 * q^76 - 104 * q^77 + 64 * q^79 - 24 * q^80 - 64 * q^82 + 16 * q^83 + 16 * q^85 + 32 * q^88 - 64 * q^91 + 40 * q^92 - 48 * q^94 - 168 * q^95 + 72 * q^97

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.bx.a	$765$	$2$	765.bx	85.o	$16$	$56$	$7$	$6.109$		None					85.2.o.a	$2$	$0$	\(8\)	\(0\)	\(8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$
765.2.bx.b	$765$	$2$	765.bx	85.o	$16$	$144$	$18$	$6.109$		None					255.2.bd.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
765.2.bx.c	$765$	$2$	765.bx	85.o	$16$	$144$	$18$	$6.109$		None		✓			765.2.bx.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(765, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(765, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)