LMFDB - Newform orbit 1323.2.a.k

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(1,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1323.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.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:	$10.5642081874$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 189)
Fricke sign:	$+1$
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Atkin-Lehner signs

$ p $	Sign
$3$	$ +1 $
$7$	$ +1 $

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by $\Q(\sqrt{-3}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1323.2.a.k		1
3.b	odd	2	1	CM	1323.2.a.k		1
7.b	odd	2	1		1323.2.a.j		1
7.c	even	3	2		189.2.e.b	✓	2
21.c	even	2	1		1323.2.a.j		1
21.h	odd	6	2		189.2.e.b	✓	2
63.g	even	3	2		567.2.g.c		2
63.h	even	3	2		567.2.h.d		2
63.j	odd	6	2		567.2.h.d		2
63.n	odd	6	2		567.2.g.c		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
189.2.e.b	✓	2	7.c	even	3	2
189.2.e.b	✓	2	21.h	odd	6	2
567.2.g.c		2	63.g	even	3	2
567.2.g.c		2	63.n	odd	6	2
567.2.h.d		2	63.h	even	3	2
567.2.h.d		2	63.j	odd	6	2
1323.2.a.j		1	7.b	odd	2	1
1323.2.a.j		1	21.c	even	2	1
1323.2.a.k		1	1.a	even	1	1	trivial
1323.2.a.k		1	3.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(1323))$:

$ T_{2} $

$ T_{5} $

$ T_{13} - 2 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T $ T
$13$	$ T - 2 $ T - 2
$17$	$ T $ T
$19$	$ T + 7 $ T + 7
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T - 11 $ T - 11
$37$	$ T + 10 $ T + 10
$41$	$ T $ T
$43$	$ T + 13 $ T + 13
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T + 13 $ T + 13
$67$	$ T + 16 $ T + 16
$71$	$ T $ T
$73$	$ T + 7 $ T + 7
$79$	$ T + 4 $ T + 4
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T - 5 $ T - 5
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Overview	Random
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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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.a (trivial)

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