LMFDB - Newform orbit 6120.2.a.p

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6120,2,Mod(1,6120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("6120.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6120 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6120.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:	$48.8684460370$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2040)
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 + q^{5} - 3 q^{7}+O(q^{10}) $

$ q + q^{5} - 3 q^{7} - 5 q^{11} - 2 q^{13} + q^{17} - 5 q^{19} + 6 q^{23} + q^{25} + 3 q^{29} + 2 q^{31} - 3 q^{35} - 7 q^{37} - q^{41} - 4 q^{43} - 3 q^{47} + 2 q^{49} + 9 q^{53} - 5 q^{55} - 4 q^{59} + 14 q^{61} - 2 q^{65} + 8 q^{67} + 4 q^{71} - 9 q^{73} + 15 q^{77} - 14 q^{79} + 4 q^{83} + q^{85} + 12 q^{89} + 6 q^{91} - 5 q^{95} - 10 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

1.00000

−3.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$3$	$ -1 $
$5$	$ -1 $
$17$	$ -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	6120.2.a.p		1
3.b	odd	2	1		2040.2.a.i	✓	1
12.b	even	2	1		4080.2.a.h		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2040.2.a.i	✓	1	3.b	odd	2	1
4080.2.a.h		1	12.b	even	2	1
6120.2.a.p		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(6120))$:

$ T_{7} + 3 $

$ T_{11} + 5 $

$ T_{13} + 2 $

$ T_{19} + 5 $

$ T_{23} - 6 $

$ T_{29} - 3 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T - 1 $ T - 1
$7$	$ T + 3 $ T + 3
$11$	$ T + 5 $ T + 5
$13$	$ T + 2 $ T + 2
$17$	$ T - 1 $ T - 1
$19$	$ T + 5 $ T + 5
$23$	$ T - 6 $ T - 6
$29$	$ T - 3 $ T - 3
$31$	$ T - 2 $ T - 2
$37$	$ T + 7 $ T + 7
$41$	$ T + 1 $ T + 1
$43$	$ T + 4 $ T + 4
$47$	$ T + 3 $ T + 3
$53$	$ T - 9 $ T - 9
$59$	$ T + 4 $ T + 4
$61$	$ T - 14 $ T - 14
$67$	$ T - 8 $ T - 8
$71$	$ T - 4 $ T - 4
$73$	$ T + 9 $ T + 9
$79$	$ T + 14 $ T + 14
$83$	$ T - 4 $ T - 4
$89$	$ T - 12 $ T - 12
$97$	$ T + 10 $ T + 10
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Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6120 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6120.a (trivial)

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