Space of modular forms of level 162, weight 2, and Character 162.g

• Label: 162.2.g
• Level: $162$
• Weight: $2$
• Character orbit: 162.g
• Rep. character: $\chi_{162}(7,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $162$
• Newform subspaces: $2$
• Sturm bound: $54$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(54\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(162, [\chi])\).

	Total	New	Old
Modular forms	522	162	360
Cusp forms	450	162	288
Eisenstein series	72	0	72

Trace form

162 * q - 9 * q^18 - 18 * q^20 - 54 * q^21 - 54 * q^23 - 54 * q^26 - 54 * q^27 - 54 * q^29 - 54 * q^30 - 54 * q^33 - 54 * q^35 - 18 * q^36 - 9 * q^38 - 18 * q^41 - 54 * q^45 - 54 * q^47 - 63 * q^51 - 54 * q^53 - 54 * q^57 - 63 * q^59 - 54 * q^63 + 18 * q^65 + 72 * q^66 - 54 * q^67 + 18 * q^68 + 126 * q^69 - 54 * q^70 + 144 * q^71 + 72 * q^72 + 144 * q^74 + 180 * q^75 - 27 * q^76 + 288 * q^77 + 144 * q^78 - 108 * q^79 + 36 * q^80 + 144 * q^81 + 144 * q^83 + 36 * q^84 - 108 * q^85 + 144 * q^86 + 288 * q^87 - 27 * q^88 + 171 * q^89 + 144 * q^90 + 72 * q^92 + 126 * q^93 - 54 * q^94 + 90 * q^95 + 18 * q^96 - 54 * q^97 + 72 * q^98 + 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(162, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
162.2.g.a	$162$	$2$	162.g	81.g	$27$	$72$	$4$	$1.294$		None		✓			162.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{27}]$
162.2.g.b	$162$	$2$	162.g	81.g	$27$	$90$	$5$	$1.294$		None		✓	✓		162.2.g.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{27}]$

Decomposition of \(S_{2}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)