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

• Label: 165.4.j
• Level: $165$
• Weight: $4$
• Character orbit: 165.j
• Rep. character: $\chi_{165}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	152	72	80
Cusp forms	136	72	64
Eisenstein series	16	0	16

Trace form

72 * q - 32 * q^5 + 56 * q^11 - 48 * q^12 - 168 * q^15 - 1264 * q^16 + 760 * q^20 - 356 * q^22 + 224 * q^23 + 592 * q^25 - 240 * q^26 + 432 * q^31 + 228 * q^33 - 2592 * q^36 + 1104 * q^37 + 2072 * q^38 + 816 * q^42 + 2400 * q^47 - 384 * q^48 - 1248 * q^53 - 380 * q^55 - 3760 * q^56 - 2992 * q^58 - 768 * q^60 + 1992 * q^66 - 464 * q^67 + 4272 * q^70 + 224 * q^71 - 720 * q^75 - 3312 * q^77 - 72 * q^78 + 8280 * q^80 - 5832 * q^81 - 2664 * q^82 + 13840 * q^86 - 3708 * q^88 - 608 * q^91 + 7360 * q^92 + 2736 * q^93 - 4104 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
165.4.j.a	$165$	$4$	165.j	55.e	$4$	$72$	$36$	$9.735$		None		✓	✓	✓	165.4.j.a	$4$	$0$	\(0\)	\(0\)	\(-32\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(165, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)