Space of modular forms of level 65, weight 2, and Character 65.m

• Label: 65.2.m
• Level: $65$
• Weight: $2$
• Character orbit: 65.m
• Rep. character: $\chi_{65}(36,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(14\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(65, [\chi])\).

	Total	New	Old
Modular forms	20	8	12
Cusp forms	12	8	4
Eisenstein series	8	0	8

Trace form

\( 8 q + 2 q^{3} + 2 q^{4} - 18 q^{6} - 6 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(65, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
65.2.m.a	$65$	$2$	65.m	13.e	$6$	$8$	$4$	$0.519$	8.0.22581504.2	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{2}+(\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(65, [\chi])\) into lower level spaces

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