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

• Label: 539.1.u
• Level: $539$
• Weight: $1$
• Character orbit: 539.u
• Rep. character: $\chi_{539}(31,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $8$
• 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.u (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
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	72	40	32
Cusp forms	8	8	0
Eisenstein series	64	32	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

8 * q + 2 * q^2 + 3 * q^4 + 2 * q^8 + q^9 + q^11 - 3 * q^18 - 4 * q^22 + 2 * q^23 + q^25 - 4 * q^29 - 4 * q^32 - 6 * q^36 - 3 * q^37 - 4 * q^43 - 2 * q^44 - q^46 - 4 * q^50 - 3 * q^53 - q^58 - 4 * q^64 + 2 * q^67 + 6 * q^71 - q^72 + 4 * q^74 - 3 * q^79 + q^81 - q^86 - q^88 + 8 * q^92 + 8 * 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.u.a	$539$	$1$	539.u	77.p	$30$	$8$	$1$	$0.269$	\(\Q(\zeta_{15})\)	$D_{5}$	\(\Q(\sqrt{-7}) \)	None			✓	✓	77.1.j.a	$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{30}^{8}-\zeta_{30}^{11})q^{2}+(-\zeta_{30}+\zeta_{30}^{4}+\cdots)q^{4}+\cdots\)