LMFDB - Newform orbit 2646.2.a.x

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, 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("2646.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.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:	$21.1284163748$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
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^{2} + q^{4} + q^{8}+O(q^{10}) $

$ q + q^{2} + q^{4} + q^{8} - 6 q^{11} + 5 q^{13} + q^{16} - 6 q^{17} - 4 q^{19} - 6 q^{22} - 6 q^{23} - 5 q^{25} + 5 q^{26} - 6 q^{29} - q^{31} + q^{32} - 6 q^{34} - q^{37} - 4 q^{38} + 6 q^{41} - q^{43} - 6 q^{44} - 6 q^{46} + 6 q^{47} - 5 q^{50} + 5 q^{52} + 6 q^{53} - 6 q^{58} + 6 q^{59} - q^{61} - q^{62} + q^{64} - q^{67} - 6 q^{68} - 12 q^{71} + 2 q^{73} - q^{74} - 4 q^{76} - q^{79} + 6 q^{82} - 6 q^{83} - q^{86} - 6 q^{88} - 6 q^{92} + 6 q^{94} + 17 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 $
$7$	$ +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	2646.2.a.x		1
3.b	odd	2	1		2646.2.a.h		1
7.b	odd	2	1		2646.2.a.w		1
7.c	even	3	2		378.2.g.b	✓	2
21.c	even	2	1		2646.2.a.g		1
21.h	odd	6	2		378.2.g.e	yes	2
63.g	even	3	2		1134.2.h.d		2
63.h	even	3	2		1134.2.e.m		2
63.j	odd	6	2		1134.2.e.c		2
63.n	odd	6	2		1134.2.h.n		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
378.2.g.b	✓	2	7.c	even	3	2
378.2.g.e	yes	2	21.h	odd	6	2
1134.2.e.c		2	63.j	odd	6	2
1134.2.e.m		2	63.h	even	3	2
1134.2.h.d		2	63.g	even	3	2
1134.2.h.n		2	63.n	odd	6	2
2646.2.a.g		1	21.c	even	2	1
2646.2.a.h		1	3.b	odd	2	1
2646.2.a.w		1	7.b	odd	2	1
2646.2.a.x		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 $S_{2}^{\mathrm{new}}(\Gamma_0(2646))$:

$ T_{5} $

$ T_{11} + 6 $

$ T_{13} - 5 $

$ T_{17} + 6 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 1 $ T - 1
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T + 6 $ T + 6
$13$	$ T - 5 $ T - 5
$17$	$ T + 6 $ T + 6
$19$	$ T + 4 $ T + 4
$23$	$ T + 6 $ T + 6
$29$	$ T + 6 $ T + 6
$31$	$ T + 1 $ T + 1
$37$	$ T + 1 $ T + 1
$41$	$ T - 6 $ T - 6
$43$	$ T + 1 $ T + 1
$47$	$ T - 6 $ T - 6
$53$	$ T - 6 $ T - 6
$59$	$ T - 6 $ T - 6
$61$	$ T + 1 $ T + 1
$67$	$ T + 1 $ T + 1
$71$	$ T + 12 $ T + 12
$73$	$ T - 2 $ T - 2
$79$	$ T + 1 $ T + 1
$83$	$ T + 6 $ T + 6
$89$	$ T $ T
$97$	$ T - 17 $ T - 17
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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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.a (trivial)

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