LMFDB - Newform orbit 2548.1.c.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,1,Mod(883,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2548.883");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2548.c (of order $2$, degree $1$, minimal)

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:	$1.27161765219$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 364)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.2548.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.25969216.1

$q$-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} + q^{9}+O(q^{10}) $

$ q - q^{2} + q^{4} - q^{8} + q^{9} + q^{11} + q^{13} + q^{16} - q^{17} - q^{18} + q^{19} - q^{22} + q^{25} - q^{26} - q^{29} - 2 q^{31} - q^{32} + q^{34} + q^{36} - q^{38} + q^{44} + q^{47} - q^{50} + q^{52} - q^{53} + q^{58} + q^{59} - q^{61} + 2 q^{62} + q^{64} + q^{67} - q^{68} + q^{71} - q^{72} + q^{76} + q^{81} - 2 q^{83} - q^{88} - q^{94} + q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$-1$	$1$	$-1$

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} $

883.1

−1.00000

1.00000

−1.00000

1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
52.b	odd	2	1	CM by $\Q(\sqrt{-13}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2548.1.c.b		1
4.b	odd	2	1		2548.1.c.d		1
7.b	odd	2	1		2548.1.c.a		1
7.c	even	3	2		364.1.bl.b	yes	2
7.d	odd	6	2		2548.1.bl.b		2
13.b	even	2	1		2548.1.c.d		1
21.h	odd	6	2		3276.1.fx.a		2
28.d	even	2	1		2548.1.c.c		1
28.f	even	6	2		2548.1.bl.a		2
28.g	odd	6	2		364.1.bl.a	✓	2
52.b	odd	2	1	CM	2548.1.c.b		1
84.n	even	6	2		3276.1.fx.b		2
91.b	odd	2	1		2548.1.c.c		1
91.r	even	6	2		364.1.bl.a	✓	2
91.s	odd	6	2		2548.1.bl.a		2
273.w	odd	6	2		3276.1.fx.b		2
364.h	even	2	1		2548.1.c.a		1
364.x	even	6	2		2548.1.bl.b		2
364.bl	odd	6	2		364.1.bl.b	yes	2
1092.by	even	6	2		3276.1.fx.a		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
364.1.bl.a	✓	2	28.g	odd	6	2
364.1.bl.a	✓	2	91.r	even	6	2
364.1.bl.b	yes	2	7.c	even	3	2
364.1.bl.b	yes	2	364.bl	odd	6	2
2548.1.c.a		1	7.b	odd	2	1
2548.1.c.a		1	364.h	even	2	1
2548.1.c.b		1	1.a	even	1	1	trivial
2548.1.c.b		1	52.b	odd	2	1	CM
2548.1.c.c		1	28.d	even	2	1
2548.1.c.c		1	91.b	odd	2	1
2548.1.c.d		1	4.b	odd	2	1
2548.1.c.d		1	13.b	even	2	1
2548.1.bl.a		2	28.f	even	6	2
2548.1.bl.a		2	91.s	odd	6	2
2548.1.bl.b		2	7.d	odd	6	2
2548.1.bl.b		2	364.x	even	6	2
3276.1.fx.a		2	21.h	odd	6	2
3276.1.fx.a		2	1092.by	even	6	2
3276.1.fx.b		2	84.n	even	6	2
3276.1.fx.b		2	273.w	odd	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(2548, [\chi])$:

$ T_{5} $

$ T_{11} - 1 $

$ T_{17} + 1 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 1 $ T + 1
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T - 1 $ T - 1
$13$	$ T - 1 $ T - 1
$17$	$ T + 1 $ T + 1
$19$	$ T - 1 $ T - 1
$23$	$ T $ T
$29$	$ T + 1 $ T + 1
$31$	$ T + 2 $ T + 2
$37$	$ T $ T
$41$	$ T $ T
$43$	$ T $ T
$47$	$ T - 1 $ T - 1
$53$	$ T + 1 $ T + 1
$59$	$ T - 1 $ T - 1
$61$	$ T + 1 $ T + 1
$67$	$ T - 1 $ T - 1
$71$	$ T - 1 $ T - 1
$73$	$ T $ T
$79$	$ T $ T
$83$	$ T + 2 $ T + 2
$89$	$ T $ T
$97$	$ T $ T
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Elliptic curves over $\Q$
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Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2548.c (of order \(2\), degree \(1\), minimal)

\(n\)	\(197\)	\(885\)	\(1275\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)

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