Space of modular forms of level 162, weight 4, and Character 162.g

• Label: 162.4.g
• Level: $162$
• Weight: $4$
• Character orbit: 162.g
• Rep. character: $\chi_{162}(7,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $486$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(162, [\chi])\).

	Total	New	Old
Modular forms	1494	486	1008
Cusp forms	1422	486	936
Eisenstein series	72	0	72

Trace form

\( 486 q + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
162.4.g.a	$162$	$4$	162.g	81.g	$27$	$234$	$13$	$9.558$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{27}]$
162.4.g.b	$162$	$4$	162.g	81.g	$27$	$252$	$14$	$9.558$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{27}]$

Decomposition of \(S_{4}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

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