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

• Label: 765.2.be
• Level: $765$
• Weight: $2$
• Character orbit: 765.be
• Rep. character: $\chi_{765}(406,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $120$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.be (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	464	120	344
Cusp forms	400	120	280
Eisenstein series	64	0	64

Trace form

120 * q + 8 * q^11 - 120 * q^16 - 8 * q^17 + 24 * q^19 + 64 * q^22 + 32 * q^23 + 16 * q^26 - 48 * q^28 - 8 * q^29 + 32 * q^34 + 32 * q^35 - 40 * q^37 - 16 * q^40 - 32 * q^41 + 40 * q^43 - 48 * q^44 - 56 * q^46 - 32 * q^49 - 8 * q^50 - 48 * q^52 - 40 * q^53 - 96 * q^56 + 64 * q^58 + 16 * q^59 + 64 * q^61 + 64 * q^62 - 8 * q^65 + 16 * q^67 - 40 * q^68 + 40 * q^71 + 160 * q^74 + 56 * q^76 + 72 * q^77 + 32 * q^79 - 32 * q^80 + 112 * q^82 + 48 * q^83 - 16 * q^86 - 136 * q^88 + 40 * q^91 - 144 * q^92 - 56 * q^94 + 16 * q^95 - 104 * 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.be.a	$765$	$2$	765.be	17.d	$8$	$16$	$4$	$6.109$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					255.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\beta _{7}-\beta _{10}-\beta _{11}+\beta _{12}+\beta _{13}+\cdots)q^{2}+\cdots\)
765.2.be.b	$765$	$2$	765.be	17.d	$8$	$24$	$6$	$6.109$		None					85.2.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
765.2.be.c	$765$	$2$	765.be	17.d	$8$	$32$	$8$	$6.109$		None					255.2.w.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{8}]$
765.2.be.d	$765$	$2$	765.be	17.d	$8$	$48$	$12$	$6.109$		None		✓	✓		765.2.be.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(765, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)