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

• Label: 165.2.d
• Level: $165$
• Weight: $2$
• Character orbit: 165.d
• Rep. character: $\chi_{165}(164,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 165 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

Trace form

\( 20 q - 24 q^{4} - 10 q^{9} + O(q^{10}) \)

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.d.a	$165$	$2$	165.d	165.d	$2$	$2$	$2$	$1.318$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}+2q^{4}+(1+\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
165.2.d.b	$165$	$2$	165.d	165.d	$2$	$2$	$2$	$1.318$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}+2q^{4}+(-2+\beta )q^{5}+(-3+\cdots)q^{9}+\cdots\)
165.2.d.c	$165$	$2$	165.d	165.d	$2$	$16$	$16$	$1.318$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)