Space of modular forms of level 165, weight 6, and Character 165.c

• Label: 165.6.c
• Level: $165$
• Weight: $6$
• Character orbit: 165.c
• Rep. character: $\chi_{165}(34,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(165, [\chi])\).

	Total	New	Old
Modular forms	124	52	72
Cusp forms	116	52	64
Eisenstein series	8	0	8

Trace form

\( 52 q - 876 q^{4} - 196 q^{5} + 180 q^{6} - 4212 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(165, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.6.c.a	$165$	$6$	165.c	5.b	$2$	$26$	$26$	$26.463$		None		$2$	$0$	\(0\)	\(0\)	\(-98\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
165.6.c.b	$165$	$6$	165.c	5.b	$2$	$26$	$26$	$26.463$		None		$2$	$0$	\(0\)	\(0\)	\(-98\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)