Space of modular forms of level 135, weight 2, and Character 135.k

• Label: 135.2.k
• Level: $135$
• Weight: $2$
• Character orbit: 135.k
• Rep. character: $\chi_{135}(16,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.k (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(135, [\chi])\).

	Total	New	Old
Modular forms	120	72	48
Cusp forms	96	72	24
Eisenstein series	24	0	24

Trace form

\( 72 q - 6 q^{6} - 18 q^{8} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(135, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
135.2.k.a	$135$	$2$	135.k	27.e	$9$	$30$	$5$	$1.078$		None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
135.2.k.b	$135$	$2$	135.k	27.e	$9$	$42$	$7$	$1.078$		None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(135, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)