Space of modular forms of level 165, weight 2, and Character 165.r

• Label: 165.2.r
• Level: $165$
• Weight: $2$
• Character orbit: 165.r
• Rep. character: $\chi_{165}(29,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.r (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 165 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(165, [\chi])\).

	Total	New	Old
Modular forms	112	112	0
Cusp forms	80	80	0
Eisenstein series	32	32	0

Trace form

\( 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(165, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.2.r.a	$165$	$2$	165.r	165.r	$10$	$80$	$20$	$1.318$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$