Space of modular forms of level 1539, weight 1, and Character 1539.o

• Label: 1539.1.o
• Level: $1539$
• Weight: $1$
• Character orbit: 1539.o
• Rep. character: $\chi_{1539}(379,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $180$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1539 = 3^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1539.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1539, [\chi])\).

	Total	New	Old
Modular forms	54	14	40
Cusp forms	30	10	20
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

\( 10 q - 5 q^{4} + 2 q^{7} - 5 q^{16} - 2 q^{19} - 3 q^{25} - 4 q^{28} + 2 q^{43} - 3 q^{49} - 8 q^{55} + 2 q^{61} + 10 q^{64} - 4 q^{73} + q^{76} + 4 q^{85}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1539, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1539.1.o.a	$1539$	$1$	1539.o	171.o	$6$	$2$	$1$	$0.768$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None		✓			1539.1.c.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}q^{11}+\cdots\)
1539.1.o.b	$1539$	$1$	1539.o	171.o	$6$	$2$	$1$	$0.768$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{57}) \)					171.1.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}q^{16}-q^{19}+\cdots\)
1539.1.o.c	$1539$	$1$	1539.o	171.o	$6$	$2$	$1$	$0.768$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None		✓			1539.1.c.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{11}+\cdots\)
1539.1.o.d	$1539$	$1$	1539.o	171.o	$6$	$4$	$2$	$0.768$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None		✓	✓		1539.1.c.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$		\(q-\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{7}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1539, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1539, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(513, [\chi])\)\(^{\oplus 2}\)