LMFDB - Newform orbit 588.3.c.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,3,Mod(197,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("588.197");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.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:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$1$

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} $

197.1

−3.00000

9.00000

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	588.3.c.a		1
3.b	odd	2	1	CM	588.3.c.a		1
7.b	odd	2	1		588.3.c.b		1
7.c	even	3	2		84.3.p.a	✓	2
7.d	odd	6	2		588.3.p.a		2
21.c	even	2	1		588.3.c.b		1
21.g	even	6	2		588.3.p.a		2
21.h	odd	6	2		84.3.p.a	✓	2
28.g	odd	6	2		336.3.bn.a		2
84.n	even	6	2		336.3.bn.a		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
84.3.p.a	✓	2	7.c	even	3	2
84.3.p.a	✓	2	21.h	odd	6	2
336.3.bn.a		2	28.g	odd	6	2
336.3.bn.a		2	84.n	even	6	2
588.3.c.a		1	1.a	even	1	1	trivial
588.3.c.a		1	3.b	odd	2	1	CM
588.3.c.b		1	7.b	odd	2	1
588.3.c.b		1	21.c	even	2	1
588.3.p.a		2	7.d	odd	6	2
588.3.p.a		2	21.g	even	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{3}^{\mathrm{new}}(588, [\chi])$:

$ T_{5} $

$ T_{13} + 1 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 3 $ T + 3
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T $ T
$13$	$ T + 1 $ T + 1
$17$	$ T $ T
$19$	$ T + 37 $ T + 37
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T - 59 $ T - 59
$37$	$ T - 47 $ T - 47
$41$	$ T $ T
$43$	$ T - 83 $ T - 83
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T - 74 $ T - 74
$67$	$ T + 109 $ T + 109
$71$	$ T $ T
$73$	$ T - 143 $ T - 143
$79$	$ T - 131 $ T - 131
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T - 2 $ T - 2
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Elliptic curves over $\Q$
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Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.c (of order \(2\), degree \(1\), minimal)

\(n\)	\(197\)	\(295\)	\(493\)
\(\chi(n)\)	\(-1\)	\(1\)	\(1\)

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