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

• Label: 540.2.n
• Level: $540$
• Weight: $2$
• Character orbit: 540.n
• Rep. character: $\chi_{540}(179,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 180 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	240	80	160
Cusp forms	192	64	128
Eisenstein series	48	16	32

Trace form

64 * q - 2 * q^4 + 6 * q^5 + 6 * q^14 - 2 * q^16 + 24 * q^20 - 2 * q^25 + 24 * q^29 - 12 * q^34 - 6 * q^40 + 12 * q^41 - 4 * q^46 - 12 * q^49 + 42 * q^50 - 78 * q^56 - 4 * q^61 - 20 * q^64 + 30 * q^65 - 16 * q^70 - 48 * q^74 - 12 * q^85 - 108 * q^86 - 34 * q^94

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.n.a	$540$	$2$	540.n	180.n	$6$	$4$	$2$	$4.312$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					180.2.n.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
540.2.n.b	$540$	$2$	540.n	180.n	$6$	$4$	$2$	$4.312$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					180.2.n.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
540.2.n.c	$540$	$2$	540.n	180.n	$6$	$8$	$4$	$4.312$	8.0.3317760000.8	\(\Q(\sqrt{-5}) \)					180.2.n.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(\beta _{4}+\beta _{5})q^{2}+(2-2\beta _{3})q^{4}+\beta _{6}q^{5}+\cdots\)
540.2.n.d	$540$	$2$	540.n	180.n	$6$	$48$	$24$	$4.312$		None			✓		180.2.n.d	$8$	$0$	\(0\)	\(0\)	\(18\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(540, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)