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

• Label: 540.2.bd
• Level: $540$
• Weight: $2$
• Character orbit: 540.bd
• Rep. character: $\chi_{540}(49,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $108$
• 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.bd (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 135 \)
Character field:			\(\Q(\zeta_{18})\)
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	684	108	576
Cusp forms	612	108	504
Eisenstein series	72	0	72

Trace form

108 * q - 3 * q^5 - 6 * q^9 + 6 * q^11 + 9 * q^15 + 36 * q^21 + 9 * q^25 + 6 * q^29 - 18 * q^31 - 9 * q^35 + 42 * q^39 + 24 * q^41 - 21 * q^45 + 18 * q^49 + 84 * q^51 - 66 * q^59 - 18 * q^61 - 69 * q^65 + 12 * q^69 - 33 * q^75 + 36 * q^79 + 6 * q^81 - 42 * q^89 - 90 * q^95 - 72 * q^99

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.bd.a	$540$	$2$	540.bd	135.p	$18$	$108$	$18$	$4.312$		None		✓	✓	✓	540.2.bd.a	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

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