Space of modular forms of level 165, weight 4, and Character 165.d

• Label: 165.4.d
• Level: $165$
• Weight: $4$
• Character orbit: 165.d
• Rep. character: $\chi_{165}(164,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(165, [\chi])\).

	Total	New	Old
Modular forms	76	76	0
Cusp forms	68	68	0
Eisenstein series	8	8	0

Trace form

\( 68 q - 264 q^{4} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(165, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.4.d.a	$165$	$4$	165.d	165.d	$2$	$2$	$2$	$9.735$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-8\)	\(18\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(-4-\beta )q^{3}+8q^{4}+(9+2\beta )q^{5}+\cdots\)
165.4.d.b	$165$	$4$	165.d	165.d	$2$	$2$	$2$	$9.735$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(8\)	\(-18\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(4+\beta )q^{3}+8q^{4}+(-9+2\beta )q^{5}+\cdots\)
165.4.d.c	$165$	$4$	165.d	165.d	$2$	$64$	$64$	$9.735$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$