Newform orbit 1584.1.j.a

• Label: 1584.1.j.a
• Level: $1584$
• Weight: $1$
• Character orbit: 1584.j
• Self dual: yes
• Analytic conductor: $0.791$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -11
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1584.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.790518980011\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 44)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.44.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.836352.1

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{5}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times\).

\(n\)	\(145\)	\(353\)	\(991\)	\(1189\)
\(\chi(n)\)	\(-1\)	\(1\)	\(1\)	\(1\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1297.1

0

0

0

0

1.00000

0

0

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	CM by \(\Q(\sqrt{-11}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1584.1.j.a		1
3.b	odd	2	1		176.1.h.a		1
4.b	odd	2	1		396.1.f.a		1
11.b	odd	2	1	CM	1584.1.j.a		1
12.b	even	2	1		44.1.d.a	✓	1
24.f	even	2	1		704.1.h.b		1
24.h	odd	2	1		704.1.h.a		1
33.d	even	2	1		176.1.h.a		1
33.f	even	10	4		1936.1.n.a		4
33.h	odd	10	4		1936.1.n.a		4
36.f	odd	6	2		3564.1.m.a		2
36.h	even	6	2		3564.1.m.b		2
44.c	even	2	1		396.1.f.a		1
48.i	odd	4	2		2816.1.b.a		2
48.k	even	4	2		2816.1.b.b		2
60.h	even	2	1		1100.1.f.a		1
60.l	odd	4	2		1100.1.e.a		2
84.h	odd	2	1		2156.1.h.a		1
84.j	odd	6	2		2156.1.k.a		2
84.n	even	6	2		2156.1.k.b		2
132.d	odd	2	1		44.1.d.a	✓	1
132.n	odd	10	4		484.1.f.a		4
132.o	even	10	4		484.1.f.a		4
264.m	even	2	1		704.1.h.a		1
264.p	odd	2	1		704.1.h.b		1
396.k	even	6	2		3564.1.m.a		2
396.o	odd	6	2		3564.1.m.b		2
528.s	odd	4	2		2816.1.b.b		2
528.x	even	4	2		2816.1.b.a		2
660.g	odd	2	1		1100.1.f.a		1
660.q	even	4	2		1100.1.e.a		2
924.n	even	2	1		2156.1.h.a		1
924.y	even	6	2		2156.1.k.a		2
924.z	odd	6	2		2156.1.k.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
44.1.d.a	✓	1	12.b	even	2	1
44.1.d.a	✓	1	132.d	odd	2	1
176.1.h.a		1	3.b	odd	2	1
176.1.h.a		1	33.d	even	2	1
396.1.f.a		1	4.b	odd	2	1
396.1.f.a		1	44.c	even	2	1
484.1.f.a		4	132.n	odd	10	4
484.1.f.a		4	132.o	even	10	4
704.1.h.a		1	24.h	odd	2	1
704.1.h.a		1	264.m	even	2	1
704.1.h.b		1	24.f	even	2	1
704.1.h.b		1	264.p	odd	2	1
1100.1.e.a		2	60.l	odd	4	2
1100.1.e.a		2	660.q	even	4	2
1100.1.f.a		1	60.h	even	2	1
1100.1.f.a		1	660.g	odd	2	1
1584.1.j.a		1	1.a	even	1	1	trivial
1584.1.j.a		1	11.b	odd	2	1	CM
1936.1.n.a		4	33.f	even	10	4
1936.1.n.a		4	33.h	odd	10	4
2156.1.h.a		1	84.h	odd	2	1
2156.1.h.a		1	924.n	even	2	1
2156.1.k.a		2	84.j	odd	6	2
2156.1.k.a		2	924.y	even	6	2
2156.1.k.b		2	84.n	even	6	2
2156.1.k.b		2	924.z	odd	6	2
2816.1.b.a		2	48.i	odd	4	2
2816.1.b.a		2	528.x	even	4	2
2816.1.b.b		2	48.k	even	4	2
2816.1.b.b		2	528.s	odd	4	2
3564.1.m.a		2	36.f	odd	6	2
3564.1.m.a		2	396.k	even	6	2
3564.1.m.b		2	36.h	even	6	2
3564.1.m.b		2	396.o	odd	6	2

Hecke kernels

This newform subspace is the entire newspace \(S_{1}^{\mathrm{new}}(1584, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T \)
$5$	\( T - 1 \)
$7$	\( T \)
$11$	\( T - 1 \)