Space of modular forms of level 165, weight 1, and Character 165.l

• Label: 165.1.l
• Level: $165$
• Weight: $1$
• Character orbit: 165.l
• Rep. character: $\chi_{165}(32,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	165.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 165 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(165, [\chi])\).

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

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 2 q^{3} + 2 q^{12} - 2 q^{15} - 4 q^{16} - 4 q^{25} - 2 q^{27} + 2 q^{33} + 4 q^{37} + 2 q^{48} + 4 q^{55} + 2 q^{60} - 4 q^{67} + 2 q^{75} + 4 q^{81} - 4 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.1.l.a	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		✓			165.1.l.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-q^{3}+i q^{4}+i q^{5}+q^{9}-i q^{11}+\cdots\)
165.1.l.b	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		✓			165.1.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{3}+i q^{4}-i q^{5}-q^{9}+i q^{11}+\cdots\)