Space of modular forms of level 540, weight 3, and Character 540.t

• Label: 540.3.t
• Level: $540$
• Weight: $3$
• Character orbit: 540.t
• Rep. character: $\chi_{540}(89,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $324$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	540.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(324\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(540, [\chi])\).

	Total	New	Old
Modular forms	468	24	444
Cusp forms	396	24	372
Eisenstein series	72	0	72

Trace form

\( 24 q + 9 q^{5} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(540, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
540.3.t.a	$540$	$3$	540.t	45.h	$6$	$24$	$12$	$14.714$		None		$4$	$0$	\(0\)	\(0\)	\(9\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

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