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

• Label: 162.2.e
• Level: $162$
• Weight: $2$
• Character orbit: 162.e
• Rep. character: $\chi_{162}(19,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $18$
• 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.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
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	198	18	180
Cusp forms	126	18	108
Eisenstein series	72	0	72

Trace form

18 * q + 6 * q^5 + 3 * q^8 + 15 * q^11 + 6 * q^14 + 12 * q^17 - 12 * q^20 - 9 * q^22 - 24 * q^23 - 18 * q^25 - 36 * q^26 - 30 * q^29 - 18 * q^31 - 9 * q^34 - 6 * q^35 + 12 * q^38 + 15 * q^41 - 9 * q^43 + 6 * q^44 - 18 * q^49 + 36 * q^50 + 24 * q^53 + 6 * q^56 - 6 * q^59 - 18 * q^61 + 24 * q^62 - 9 * q^64 - 6 * q^65 + 27 * q^67 + 12 * q^68 + 36 * q^70 - 24 * q^71 - 18 * q^73 - 30 * q^74 + 18 * q^76 - 42 * q^77 + 72 * q^79 - 12 * q^80 + 72 * q^85 - 27 * q^86 + 18 * q^88 + 3 * q^89 - 18 * q^91 - 6 * q^92 + 36 * q^94 - 6 * q^95 + 27 * q^97 + 15 * q^98

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.e.a	$162$	$2$	162.e	27.e	$9$	$6$	$1$	$1.294$	\(\Q(\zeta_{18})\)	None					54.2.e.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
162.2.e.b	$162$	$2$	162.e	27.e	$9$	$12$	$2$	$1.294$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None			✓		54.2.e.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)	$3^{3}$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{4}+\beta _{8})q^{2}-\beta _{6}q^{4}+(1-\beta _{2}+\beta _{7}+\cdots)q^{5}+\cdots\)

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

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