Space of modular forms of level 162, weight 3, and Character 162.d

• Label: 162.3.d
• Level: $162$
• Weight: $3$
• Character orbit: 162.d
• Rep. character: $\chi_{162}(53,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $81$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(81\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(162, [\chi])\).

	Total	New	Old
Modular forms	132	16	116
Cusp forms	84	16	68
Eisenstein series	48	0	48

Trace form

16 * q + 16 * q^4 - 10 * q^7 + 50 * q^13 - 32 * q^16 + 164 * q^19 + 24 * q^22 + 52 * q^25 - 40 * q^28 - 100 * q^31 - 48 * q^34 - 388 * q^37 + 140 * q^43 + 48 * q^46 - 138 * q^49 - 100 * q^52 + 144 * q^55 - 120 * q^58 - 94 * q^61 - 128 * q^64 + 62 * q^67 + 360 * q^70 - 4 * q^73 + 164 * q^76 - 106 * q^79 - 216 * q^82 - 144 * q^85 - 48 * q^88 + 28 * q^91 - 168 * q^94 - 286 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(162, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
162.3.d.a	$162$	$3$	162.d	9.d	$6$	$4$	$2$	$4.414$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					54.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-6\beta _{1}+6\beta _{3})q^{5}+\cdots\)
162.3.d.b	$162$	$3$	162.d	9.d	$6$	$4$	$2$	$4.414$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					18.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(3\beta _{1}-3\beta _{3})q^{5}+\cdots\)
162.3.d.c	$162$	$3$	162.d	9.d	$6$	$8$	$4$	$4.414$	\(\Q(\zeta_{24})\)	None		✓	✓		162.3.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_{5} q^{2}+2\beta_1 q^{4}+(\beta_{7}-\beta_{6}+2\beta_{3})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)