Space of modular forms of level 539, weight 1, and Character 539.l

• Label: 539.1.l
• Level: $539$
• Weight: $1$
• Character orbit: 539.l
• Rep. character: $\chi_{539}(50,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	539.l (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(539, [\chi])\).

	Total	New	Old
Modular forms	36	24	12
Cusp forms	4	4	0
Eisenstein series	32	20	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 - q^4 - 5 * q^8 + q^9 - q^11 - 6 * q^16 + 5 * q^18 + 2 * q^23 + q^25 + q^36 + 3 * q^37 + 4 * q^44 - 5 * q^46 - 3 * q^53 + 5 * q^58 + 4 * q^64 + 2 * q^67 - 3 * q^71 - 5 * q^72 - 5 * q^79 - q^81 - 5 * q^86 + 5 * q^88 + 2 * q^92 - 4 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(539, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
539.1.l.a	$539$	$1$	539.l	11.d	$10$	$4$	$1$	$0.269$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-7}) \)	None		✓	✓	✓	539.1.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{10}+\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots\)