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

• Label: 540.2.u
• Level: $540$
• Weight: $2$
• Character orbit: 540.u
• Rep. character: $\chi_{540}(61,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.u (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	684	72	612
Cusp forms	612	72	540
Eisenstein series	72	0	72

Trace form

72 * q - 6 * q^9 + 24 * q^17 + 24 * q^21 + 36 * q^23 + 42 * q^27 + 42 * q^29 + 42 * q^33 + 12 * q^35 + 12 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 72 * q^47 + 18 * q^49 - 42 * q^51 - 72 * q^53 - 90 * q^57 - 42 * q^59 + 18 * q^61 - 72 * q^63 + 12 * q^65 + 18 * q^67 + 6 * q^69 + 24 * q^71 - 18 * q^73 + 6 * q^77 + 36 * q^79 + 66 * q^81 + 30 * q^83 + 36 * q^85 - 30 * q^87 - 6 * q^89 - 18 * q^91 + 18 * q^93 + 24 * q^95 + 18 * q^97 - 102 * 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.u.a	$540$	$2$	540.u	27.e	$9$	$30$	$5$	$4.312$		None		✓			540.2.u.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
540.2.u.b	$540$	$2$	540.u	27.e	$9$	$42$	$7$	$4.312$		None		✓	✓		540.2.u.b	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

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

\( S_{2}^{\mathrm{old}}(540, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)