LMFDB - Newform orbit 816.3.m.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,3,Mod(305,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("816.305");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	816.m (of order $2$, degree $1$, not 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:	$22.2343895718$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
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 $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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} $

305.1

3.00000

7.00000

9.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
51.c	odd	2	1	CM by $\Q(\sqrt{-51}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	816.3.m.b		1
3.b	odd	2	1		816.3.m.a		1
4.b	odd	2	1		51.3.c.a	✓	1
12.b	even	2	1		51.3.c.b	yes	1
17.b	even	2	1		816.3.m.a		1
51.c	odd	2	1	CM	816.3.m.b		1
68.d	odd	2	1		51.3.c.b	yes	1
204.h	even	2	1		51.3.c.a	✓	1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
51.3.c.a	✓	1	4.b	odd	2	1
51.3.c.a	✓	1	204.h	even	2	1
51.3.c.b	yes	1	12.b	even	2	1
51.3.c.b	yes	1	68.d	odd	2	1
816.3.m.a		1	3.b	odd	2	1
816.3.m.a		1	17.b	even	2	1
816.3.m.b		1	1.a	even	1	1	trivial
816.3.m.b		1	51.c	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5} - 7 $ T5 - 7 acting on $S_{3}^{\mathrm{new}}(816, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 3 $ T - 3
$5$	$ T - 7 $ T - 7
$7$	$ T $ T
$11$	$ T - 5 $ T - 5
$13$	$ T + 25 $ T + 25
$17$	$ T - 17 $ T - 17
$19$	$ T - 13 $ T - 13
$23$	$ T - 29 $ T - 29
$29$	$ T - 10 $ T - 10
$31$	$ T $ T
$37$	$ T $ T
$41$	$ T + 65 $ T + 65
$43$	$ T + 35 $ T + 35
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T $ T
$67$	$ T - 70 $ T - 70
$71$	$ T + 130 $ T + 130
$73$	$ T $ T
$79$	$ T $ T
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T $ T
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Overview	Random
Universe	Knowledge

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	816.m (of order \(2\), degree \(1\), not minimal)

\(n\)	\(241\)	\(511\)	\(545\)	\(613\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)	\(1\)

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