Space of modular forms of level 65, weight 3, and Character 65.p

• Label: 65.3.p
• Level: $65$
• Weight: $3$
• Character orbit: 65.p
• Rep. character: $\chi_{65}(6,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	65.p (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(65, [\chi])\).

	Total	New	Old
Modular forms	64	40	24
Cusp forms	48	40	8
Eisenstein series	16	0	16

Trace form

\( 40 q - 12 q^{6} - 40 q^{7} + 36 q^{8} - 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(65, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
65.3.p.a	$65$	$3$	65.p	13.f	$12$	$40$	$10$	$1.771$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{3}^{\mathrm{old}}(65, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(65, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)