Newform orbit 1584.3.j.a

• Label: 1584.3.j.a
• Level: $1584$
• Weight: $3$
• Character orbit: 1584.j
• Self dual: yes
• Analytic conductor: $43.161$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -11
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	yes
Analytic conductor:	\(43.1608738747\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{5} - 11 q^{11} + 35 q^{23} - 24 q^{25} + 37 q^{31} - 25 q^{37} + 50 q^{47} + 49 q^{49} + 70 q^{53} - 11 q^{55} + 107 q^{59} - 35 q^{67} - 133 q^{71} + 97 q^{89} + 95 q^{97}+O(q^{100}) \)

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	1584.3.j.a		1
3.b	odd	2	1		176.3.h.a		1
4.b	odd	2	1		99.3.c.a		1
11.b	odd	2	1	CM	1584.3.j.a		1
12.b	even	2	1		11.3.b.a	✓	1
24.f	even	2	1		704.3.h.b		1
24.h	odd	2	1		704.3.h.a		1
33.d	even	2	1		176.3.h.a		1
44.c	even	2	1		99.3.c.a		1
60.h	even	2	1		275.3.c.a		1
60.l	odd	4	2		275.3.d.a		2
84.h	odd	2	1		539.3.c.a		1
132.d	odd	2	1		11.3.b.a	✓	1
132.n	odd	10	4		121.3.d.b		4
132.o	even	10	4		121.3.d.b		4
264.m	even	2	1		704.3.h.a		1
264.p	odd	2	1		704.3.h.b		1
660.g	odd	2	1		275.3.c.a		1
660.q	even	4	2		275.3.d.a		2
924.n	even	2	1		539.3.c.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
11.3.b.a	✓	1	12.b	even	2	1
11.3.b.a	✓	1	132.d	odd	2	1
99.3.c.a		1	4.b	odd	2	1
99.3.c.a		1	44.c	even	2	1
121.3.d.b		4	132.n	odd	10	4
121.3.d.b		4	132.o	even	10	4
176.3.h.a		1	3.b	odd	2	1
176.3.h.a		1	33.d	even	2	1
275.3.c.a		1	60.h	even	2	1
275.3.c.a		1	660.g	odd	2	1
275.3.d.a		2	60.l	odd	4	2
275.3.d.a		2	660.q	even	4	2
539.3.c.a		1	84.h	odd	2	1
539.3.c.a		1	924.n	even	2	1
704.3.h.a		1	24.h	odd	2	1
704.3.h.a		1	264.m	even	2	1
704.3.h.b		1	24.f	even	2	1
704.3.h.b		1	264.p	odd	2	1
1584.3.j.a		1	1.a	even	1	1	trivial
1584.3.j.a		1	11.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(1584, [\chi])\):

\( T_{5} - 1 \)

\( T_{7} \)

Hecke characteristic polynomials

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