Space of modular forms of level 486, weight 2, and Character 486.g

• Label: 486.2.g
• Level: $486$
• Weight: $2$
• Character orbit: 486.g
• Rep. character: $\chi_{486}(19,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $162$
• Newform subspaces: $2$
• Sturm bound: $162$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.g (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(162\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(486, [\chi])\).

	Total	New	Old
Modular forms	1566	162	1404
Cusp forms	1350	162	1188
Eisenstein series	216	0	216

Trace form

162 * q + 18 * q^20 + 54 * q^23 + 54 * q^26 + 54 * q^29 + 54 * q^35 + 9 * q^38 + 18 * q^41 + 54 * q^47 + 54 * q^53 + 63 * q^59 - 18 * q^65 - 54 * q^67 - 18 * q^68 - 54 * q^70 - 144 * q^71 - 144 * q^74 - 27 * q^76 - 288 * q^77 - 108 * q^79 - 36 * q^80 - 144 * q^83 - 108 * q^85 - 144 * q^86 - 27 * q^88 - 171 * q^89 - 72 * q^92 - 54 * q^94 - 90 * q^95 - 54 * q^97 - 72 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(486, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
486.2.g.a	$486$	$2$	486.g	81.g	$27$	$72$	$4$	$3.881$		None					162.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{27}]$
486.2.g.b	$486$	$2$	486.g	81.g	$27$	$90$	$5$	$3.881$		None			✓		162.2.g.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{27}]$

Decomposition of \(S_{2}^{\mathrm{old}}(486, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(486, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 2}\)