Newform orbit 6084.2.a.c

• Label: 6084.2.a.c
• Level: $6084$
• Weight: $2$
• Character orbit: 6084.a
• Self dual: yes
• Analytic conductor: $48.581$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$6084 = 2^{2} \cdot 3^{2} \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	6084.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$48.5809845897$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 52)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 3 * q^5 + 4 * q^7 - 3 * q^17 - 2 * q^19 + 6 * q^23 + 4 * q^25 - 9 * q^29 - 2 * q^31 - 12 * q^35 + 7 * q^37 + 3 * q^41 - 4 * q^43 - 6 * q^47 + 9 * q^49 - 9 * q^53 + 5 * q^61 - 2 * q^67 - 6 * q^71 + q^73 - 4 * q^79 + 12 * q^83 + 9 * q^85 + 6 * q^89 + 6 * q^95 - 14 * q^97

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1.1

0

0

0

0

−3.00000

0

4.00000

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$13$	$+1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	6084.2.a.c		1
3.b	odd	2	1		676.2.a.b		1
12.b	even	2	1		2704.2.a.m		1
13.b	even	2	1		6084.2.a.o		1
13.d	odd	4	2		6084.2.b.k		2
13.e	even	6	2		468.2.l.d		2
39.d	odd	2	1		676.2.a.a		1
39.f	even	4	2		676.2.d.a		2
39.h	odd	6	2		52.2.e.b	✓	2
39.i	odd	6	2		676.2.e.d		2
39.k	even	12	4		676.2.h.d		4
52.i	odd	6	2		1872.2.t.m		2
156.h	even	2	1		2704.2.a.l		1
156.l	odd	4	2		2704.2.f.i		2
156.r	even	6	2		208.2.i.a		2
195.y	odd	6	2		1300.2.i.b		2
195.bf	even	12	4		1300.2.bb.d		4
273.u	even	6	2		2548.2.k.a		2
273.x	odd	6	2		2548.2.l.b		2
273.y	even	6	2		2548.2.l.g		2
273.bp	odd	6	2		2548.2.i.g		2
273.br	even	6	2		2548.2.i.b		2
312.ba	even	6	2		832.2.i.i		2
312.bg	odd	6	2		832.2.i.c		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
52.2.e.b	✓	2	39.h	odd	6	2
208.2.i.a		2	156.r	even	6	2
468.2.l.d		2	13.e	even	6	2
676.2.a.a		1	39.d	odd	2	1
676.2.a.b		1	3.b	odd	2	1
676.2.d.a		2	39.f	even	4	2
676.2.e.d		2	39.i	odd	6	2
676.2.h.d		4	39.k	even	12	4
832.2.i.c		2	312.bg	odd	6	2
832.2.i.i		2	312.ba	even	6	2
1300.2.i.b		2	195.y	odd	6	2
1300.2.bb.d		4	195.bf	even	12	4
1872.2.t.m		2	52.i	odd	6	2
2548.2.i.b		2	273.br	even	6	2
2548.2.i.g		2	273.bp	odd	6	2
2548.2.k.a		2	273.u	even	6	2
2548.2.l.b		2	273.x	odd	6	2
2548.2.l.g		2	273.y	even	6	2
2704.2.a.l		1	156.h	even	2	1
2704.2.a.m		1	12.b	even	2	1
2704.2.f.i		2	156.l	odd	4	2
6084.2.a.c		1	1.a	even	1	1	trivial
6084.2.a.o		1	13.b	even	2	1
6084.2.b.k		2	13.d	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(6084))$:

$T_{5} + 3$

$T_{7} - 4$

$T_{11}$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T + 3$
$7$	$T - 4$
$11$	$T$