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

• Label: 540.1.f
• Level: $540$
• Weight: $1$
• Character orbit: 540.f
• Rep. character: $\chi_{540}(379,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	540.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	20	4	16
Cusp forms	8	4	4
Eisenstein series	12	0	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{4} + 2 q^{10} - 2 q^{16} - 4 q^{25} + 2 q^{34} + 4 q^{40} - 6 q^{46} - 4 q^{49} + 4 q^{61} - 4 q^{64} - 6 q^{76} - 4 q^{85}+O(q^{100}) \)

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.f.a	$540$	$1$	540.f	20.d	$2$	$4$	$4$	$0.269$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None		✓	✓	✓	540.1.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(540, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)