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

• Label: 765.2.cc
• Level: $765$
• Weight: $2$
• Character orbit: 765.cc
• Rep. character: $\chi_{765}(28,\cdot)$
• 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.cc (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

\( 344 q + 8 q^{2} + 8 q^{5} - 8 q^{7} + 24 q^{8} + O(q^{10}) \)

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

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