Space of modular forms of level 540, weight 2, and Character 540.x

• Label: 540.2.x
• Level: $540$
• Weight: $2$
• Character orbit: 540.x
• Rep. character: $\chi_{540}(17,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(540, [\chi])\).

	Total	New	Old
Modular forms	504	24	480
Cusp forms	360	24	336
Eisenstein series	144	0	144

Trace form

\( 24 q - 12 q^{11} + 24 q^{23} + 6 q^{25} + 12 q^{37} + 36 q^{41} + 42 q^{47} + 12 q^{55} - 12 q^{61} + 24 q^{65} + 6 q^{67} - 96 q^{77} - 60 q^{83} - 24 q^{85} - 24 q^{91} - 60 q^{95} - 18 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(540, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
540.2.x.a	$540$	$2$	540.x	45.l	$12$	$24$	$6$	$4.312$		None			✓	✓	180.2.w.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(540, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)