LMFDB - Newform orbit 912.2.a.h

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(1,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("912.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.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:	$7.28235666434$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
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)

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

−4.00000

1.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$3$	$ -1 $
$19$	$ +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	912.2.a.h		1
3.b	odd	2	1		2736.2.a.j		1
4.b	odd	2	1		114.2.a.a	✓	1
8.b	even	2	1		3648.2.a.j		1
8.d	odd	2	1		3648.2.a.bb		1
12.b	even	2	1		342.2.a.f		1
20.d	odd	2	1		2850.2.a.x		1
20.e	even	4	2		2850.2.d.s		2
28.d	even	2	1		5586.2.a.p		1
60.h	even	2	1		8550.2.a.a		1
76.d	even	2	1		2166.2.a.i		1
228.b	odd	2	1		6498.2.a.h		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
114.2.a.a	✓	1	4.b	odd	2	1
342.2.a.f		1	12.b	even	2	1
912.2.a.h		1	1.a	even	1	1	trivial
2166.2.a.i		1	76.d	even	2	1
2736.2.a.j		1	3.b	odd	2	1
2850.2.a.x		1	20.d	odd	2	1
2850.2.d.s		2	20.e	even	4	2
3648.2.a.j		1	8.b	even	2	1
3648.2.a.bb		1	8.d	odd	2	1
5586.2.a.p		1	28.d	even	2	1
6498.2.a.h		1	228.b	odd	2	1
8550.2.a.a		1	60.h	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(912))$:

$ T_{5} $

$ T_{7} + 4 $

$ T_{11} + 4 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 1 $ T - 1
$5$	$ T $ T
$7$	$ T + 4 $ T + 4
$11$	$ T + 4 $ T + 4
$13$	$ T $ T
$17$	$ T + 2 $ T + 2
$19$	$ T + 1 $ T + 1
$23$	$ T - 2 $ T - 2
$29$	$ T + 6 $ T + 6
$31$	$ T + 6 $ T + 6
$37$	$ T + 8 $ T + 8
$41$	$ T - 10 $ T - 10
$43$	$ T - 12 $ T - 12
$47$	$ T + 10 $ T + 10
$53$	$ T - 2 $ T - 2
$59$	$ T + 4 $ T + 4
$61$	$ T + 10 $ T + 10
$67$	$ T $ T
$71$	$ T - 16 $ T - 16
$73$	$ T + 2 $ T + 2
$79$	$ T + 10 $ T + 10
$83$	$ T - 16 $ T - 16
$89$	$ T + 2 $ T + 2
$97$	$ T + 10 $ T + 10
show more
show less

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.a (trivial)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more