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}$