Space of modular forms of level 65, weight 6, and Character 65.b

• Label: 65.6.b
• Level: $65$
• Weight: $6$
• Character orbit: 65.b
• Rep. character: $\chi_{65}(14,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(65, [\chi])\).

	Total	New	Old
Modular forms	38	30	8
Cusp forms	34	30	4
Eisenstein series	4	0	4

Trace form

\( 30 q - 500 q^{4} + 80 q^{5} - 404 q^{6} - 1926 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(65, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
65.6.b.a	$65$	$6$	65.b	5.b	$2$	$30$	$30$	$10.425$		None		✓	✓	✓	65.6.b.a	$2$	$0$	\(0\)	\(0\)	\(80\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(65, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(65, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)