Space of modular forms of level 540, weight 1, and Character 540.bf

• Label: 540.1.bf
• Level: $540$
• Weight: $1$
• Character orbit: 540.bf
• Rep. character: $\chi_{540}(79,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	540.bf (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 540 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(540, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	12	12	0
Eisenstein series	24	24	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - 6 q^{6} - 6 q^{14} - 6 q^{29} - 6 q^{36} + 12 q^{41} - 6 q^{45} - 6 q^{49} - 6 q^{56} - 6 q^{61} - 6 q^{64} + 12 q^{69} + 12 q^{70} + 12 q^{80} + 12 q^{84} + 12 q^{94}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(540, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
540.1.bf.a	$540$	$1$	540.bf	540.af	$18$	$6$	$1$	$0.269$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-5}) \)	None		✓			540.1.bf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$1$		\(q-\zeta_{18}q^{2}-\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots\)
540.1.bf.b	$540$	$1$	540.bf	540.af	$18$	$6$	$1$	$0.269$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-5}) \)	None		✓			540.1.bf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q+\zeta_{18}q^{2}+\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots\)