LMFDB - Newform orbit 5040.2.a.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5040,2,Mod(1,5040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5040, 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("5040.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5040.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:	$40.2446026187$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
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} - q^{7}+O(q^{10}) $

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

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$3$	$ -1 $
$5$	$ +1 $
$7$	$ +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	5040.2.a.a		1
3.b	odd	2	1		560.2.a.f		1
4.b	odd	2	1		2520.2.a.i		1
12.b	even	2	1		280.2.a.a	✓	1
15.d	odd	2	1		2800.2.a.c		1
15.e	even	4	2		2800.2.g.b		2
21.c	even	2	1		3920.2.a.c		1
24.f	even	2	1		2240.2.a.z		1
24.h	odd	2	1		2240.2.a.a		1
60.h	even	2	1		1400.2.a.n		1
60.l	odd	4	2		1400.2.g.a		2
84.h	odd	2	1		1960.2.a.o		1
84.j	odd	6	2		1960.2.q.a		2
84.n	even	6	2		1960.2.q.o		2
420.o	odd	2	1		9800.2.a.a		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.2.a.a	✓	1	12.b	even	2	1
560.2.a.f		1	3.b	odd	2	1
1400.2.a.n		1	60.h	even	2	1
1400.2.g.a		2	60.l	odd	4	2
1960.2.a.o		1	84.h	odd	2	1
1960.2.q.a		2	84.j	odd	6	2
1960.2.q.o		2	84.n	even	6	2
2240.2.a.a		1	24.h	odd	2	1
2240.2.a.z		1	24.f	even	2	1
2520.2.a.i		1	4.b	odd	2	1
2800.2.a.c		1	15.d	odd	2	1
2800.2.g.b		2	15.e	even	4	2
3920.2.a.c		1	21.c	even	2	1
5040.2.a.a		1	1.a	even	1	1	trivial
9800.2.a.a		1	420.o	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(5040))$:

$ T_{11} + 5 $

$ T_{13} + 5 $

$ T_{17} - 7 $

$ T_{19} - 2 $

$ T_{29} + 7 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T + 1 $ T + 1
$7$	$ T + 1 $ T + 1
$11$	$ T + 5 $ T + 5
$13$	$ T + 5 $ T + 5
$17$	$ T - 7 $ T - 7
$19$	$ T - 2 $ T - 2
$23$	$ T + 2 $ T + 2
$29$	$ T + 7 $ T + 7
$31$	$ T + 4 $ T + 4
$37$	$ T + 6 $ T + 6
$41$	$ T - 12 $ T - 12
$43$	$ T - 2 $ T - 2
$47$	$ T - 1 $ T - 1
$53$	$ T $ T
$59$	$ T + 4 $ T + 4
$61$	$ T - 4 $ T - 4
$67$	$ T + 8 $ T + 8
$71$	$ T $ T
$73$	$ T - 6 $ T - 6
$79$	$ T - 3 $ T - 3
$83$	$ T + 4 $ T + 4
$89$	$ T $ T
$97$	$ T - 13 $ T - 13
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5040.a (trivial)

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