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

• Label: 135.2.j
• Level: $135$
• Weight: $2$
• Character orbit: 135.j
• Rep. character: $\chi_{135}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	48	16	32
Cusp forms	24	8	16
Eisenstein series	24	8	16

Trace form

8 * q - 8 * q^10 + 12 * q^11 + 4 * q^16 - 8 * q^19 - 12 * q^20 - 4 * q^25 - 24 * q^26 - 12 * q^29 + 4 * q^31 - 4 * q^34 + 24 * q^35 - 4 * q^40 + 24 * q^41 + 24 * q^44 - 16 * q^46 - 4 * q^49 - 24 * q^50 + 24 * q^55 + 12 * q^56 - 24 * q^59 - 8 * q^61 + 32 * q^64 + 12 * q^70 - 72 * q^71 + 12 * q^74 - 12 * q^76 + 16 * q^79 + 48 * q^80 + 16 * q^85 + 36 * q^86 + 24 * q^89 - 24 * q^91 + 20 * q^94 - 12 * q^95

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
135.2.j.a	$135$	$2$	135.j	45.j	$6$	$8$	$4$	$1.078$	\(\Q(\zeta_{24})\)	None			✓	✓	45.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_{6} q^{2}-\beta_{3} q^{4}+(\beta_{7}-\beta_{6}-\beta_{3}+\beta_1)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(135, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)