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

• Label: 165.2.p
• Level: $165$
• Weight: $2$
• Character orbit: 165.p
• Rep. character: $\chi_{165}(41,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	112	64	48
Cusp forms	80	64	16
Eisenstein series	32	0	32

Trace form

\( 64 q + 4 q^{3} - 16 q^{4} - 10 q^{6} - 18 q^{9} + O(q^{10}) \)

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.p.a	$165$	$2$	165.p	33.f	$10$	$16$	$4$	$1.318$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(-10\)	$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{2}-\beta _{5}+\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots\)
165.2.p.b	$165$	$2$	165.p	33.f	$10$	$48$	$12$	$1.318$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)