Space of modular forms of level 65, weight 4, and Character 65.o

• Label: 65.4.o
• Level: $65$
• Weight: $4$
• Character orbit: 65.o
• Rep. character: $\chi_{65}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.o (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(65, [\chi])\).

	Total	New	Old
Modular forms	92	92	0
Cusp forms	76	76	0
Eisenstein series	16	16	0

Trace form

\( 76 q - 6 q^{2} - 2 q^{3} - 136 q^{4} + 10 q^{5} - 8 q^{6} - 6 q^{7} + 120 q^{8} + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(65, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
65.4.o.a	$65$	$4$	65.o	65.o	$12$	$76$	$19$	$3.835$		None		✓	✓	✓	65.4.o.a	$2$	$0$	\(-6\)	\(-2\)	\(10\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$