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

• Label: 540.2.r
• Level: $540$
• Weight: $2$
• Character orbit: 540.r
• Rep. character: $\chi_{540}(289,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• 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.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
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	252	12	240
Cusp forms	180	12	168
Eisenstein series	72	0	72

Trace form

\( 12 q - q^{5} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
540.2.r.a	$540$	$2$	540.r	45.j	$6$	$12$	$6$	$4.312$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{5}+\beta _{10})q^{5}+(\beta _{7}-\beta _{9}+\beta _{10}+\cdots)q^{7}+\cdots\)

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

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