Newform orbit 1584.3.j.c

• Label: 1584.3.j.c
• Level: $1584$
• Weight: $3$
• Character orbit: 1584.j
• Self dual: yes
• Analytic conductor: $43.161$
• Analytic rank: $0$
• Dimension: $2$
• 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:	\(2\)
Coefficient field:	\(\Q(\sqrt{33}) \)
Defining polynomial:	\( x^{2} - x - 8 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 3 \)
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(-1 + 3\sqrt{33})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + (-b - 1) * q^5 - 11 * q^11 + (-3*b - 19) * q^23 + (b + 50) * q^25 + (-5*b - 21) * q^31 + (-7*b + 9) * q^37 + 50 * q^47 + 49 * q^49 + 70 * q^53 + (11*b + 11) * q^55 + (5*b - 51) * q^59 + (-13*b + 11) * q^67 + (5*b + 69) * q^71 + (15*b - 41) * q^89 + (17*b - 39) * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} - 22 q^{11} - 35 q^{23} + 99 q^{25} - 37 q^{31} + 25 q^{37} + 100 q^{47} + 98 q^{49} + 140 q^{53} + 11 q^{55} - 107 q^{59} + 35 q^{67} + 133 q^{71} - 97 q^{89} - 95 q^{97}+O(q^{100}) \)

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

3.37228
−2.37228

0

0

0

−9.11684

0

0

0

0

0

1297.2

0

0

0

8.11684

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.c		2
3.b	odd	2	1		176.3.h.b		2
4.b	odd	2	1		396.3.f.a		2
11.b	odd	2	1	CM	1584.3.j.c		2
12.b	even	2	1		44.3.d.a	✓	2
24.f	even	2	1		704.3.h.c		2
24.h	odd	2	1		704.3.h.f		2
33.d	even	2	1		176.3.h.b		2
44.c	even	2	1		396.3.f.a		2
60.h	even	2	1		1100.3.f.a		2
60.l	odd	4	2		1100.3.e.a		4
84.h	odd	2	1		2156.3.h.a		2
132.d	odd	2	1		44.3.d.a	✓	2
132.n	odd	10	4		484.3.f.b		8
132.o	even	10	4		484.3.f.b		8
264.m	even	2	1		704.3.h.f		2
264.p	odd	2	1		704.3.h.c		2
660.g	odd	2	1		1100.3.f.a		2
660.q	even	4	2		1100.3.e.a		4
924.n	even	2	1		2156.3.h.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
44.3.d.a	✓	2	12.b	even	2	1
44.3.d.a	✓	2	132.d	odd	2	1
176.3.h.b		2	3.b	odd	2	1
176.3.h.b		2	33.d	even	2	1
396.3.f.a		2	4.b	odd	2	1
396.3.f.a		2	44.c	even	2	1
484.3.f.b		8	132.n	odd	10	4
484.3.f.b		8	132.o	even	10	4
704.3.h.c		2	24.f	even	2	1
704.3.h.c		2	264.p	odd	2	1
704.3.h.f		2	24.h	odd	2	1
704.3.h.f		2	264.m	even	2	1
1100.3.e.a		4	60.l	odd	4	2
1100.3.e.a		4	660.q	even	4	2
1100.3.f.a		2	60.h	even	2	1
1100.3.f.a		2	660.g	odd	2	1
1584.3.j.c		2	1.a	even	1	1	trivial
1584.3.j.c		2	11.b	odd	2	1	CM
2156.3.h.a		2	84.h	odd	2	1
2156.3.h.a		2	924.n	even	2	1

Hecke kernels

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

\( T_{5}^{2} + T_{5} - 74 \)

\( T_{7} \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} + T - 74 \)
$7$	\( T^{2} \)
$11$	\( (T + 11)^{2} \)