LMFDB - Newform orbit 6084.2.a.c

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6084,2,Mod(1,6084)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6084, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6084.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q - 3 q^{5} + 4 q^{7}+O(q^{10}) $

$ 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}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

1.1

−3.00000

4.00000

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 $ T
$3$	$ T $ T
$5$	$ T + 3 $ T + 3
$7$	$ T - 4 $ T - 4
$11$	$ T $ T
$13$	$ T $ T
$17$	$ T + 3 $ T + 3
$19$	$ T + 2 $ T + 2
$23$	$ T - 6 $ T - 6
$29$	$ T + 9 $ T + 9
$31$	$ T + 2 $ T + 2
$37$	$ T - 7 $ T - 7
$41$	$ T - 3 $ T - 3
$43$	$ T + 4 $ T + 4
$47$	$ T + 6 $ T + 6
$53$	$ T + 9 $ T + 9
$59$	$ T $ T
$61$	$ T - 5 $ T - 5
$67$	$ T + 2 $ T + 2
$71$	$ T + 6 $ T + 6
$73$	$ T - 1 $ T - 1
$79$	$ T + 4 $ T + 4
$83$	$ T - 12 $ T - 12
$89$	$ T - 6 $ T - 6
$97$	$ T + 14 $ T + 14
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Overview	Random
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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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