LMFDB - Newform orbit 7448.2.a.c

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7448,2,Mod(1,7448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7448, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7448.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7448 = 2^{3} \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7448.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:	$59.4725794254$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1064)
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 - 2 q^{3} - q^{5} + q^{9} + 4 q^{11} + 2 q^{13} + 2 q^{15} - 7 q^{17} - q^{19} - 3 q^{23} - 4 q^{25} + 4 q^{27} + 4 q^{29} + 4 q^{31} - 8 q^{33} + 10 q^{37} - 4 q^{39} - 9 q^{43} - q^{45} - 4 q^{47}+ \cdots + 4 q^{99}+O(q^{100}) $

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

−2.00000

−1.00000

1.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$7$	$ +1 $
$19$	$ +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	7448.2.a.c		1
7.b	odd	2	1		7448.2.a.v		1
7.c	even	3	2		1064.2.q.j	✓	2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1064.2.q.j	✓	2	7.c	even	3	2
7448.2.a.c		1	1.a	even	1	1	trivial
7448.2.a.v		1	7.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(7448))$:

$ T_{3} + 2 $

$ T_{5} + 1 $

$ T_{11} - 4 $

$ T_{13} - 2 $

$ T_{17} + 7 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 2 $ T + 2
$5$	$ T + 1 $ T + 1
$7$	$ T $ T
$11$	$ T - 4 $ T - 4
$13$	$ T - 2 $ T - 2
$17$	$ T + 7 $ T + 7
$19$	$ T + 1 $ T + 1
$23$	$ T + 3 $ T + 3
$29$	$ T - 4 $ T - 4
$31$	$ T - 4 $ T - 4
$37$	$ T - 10 $ T - 10
$41$	$ T $ T
$43$	$ T + 9 $ T + 9
$47$	$ T + 4 $ T + 4
$53$	$ T - 6 $ T - 6
$59$	$ T + 12 $ T + 12
$61$	$ T + 2 $ T + 2
$67$	$ T - 16 $ T - 16
$71$	$ T - 6 $ T - 6
$73$	$ T - 2 $ T - 2
$79$	$ T - 4 $ T - 4
$83$	$ T + 9 $ T + 9
$89$	$ T + 4 $ T + 4
$97$	$ T + 4 $ T + 4
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7448.a (trivial)

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