LMFDB - Newform orbit 784.4.a.i

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,4,Mod(1,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("784.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	784.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:	$46.2574974445$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 56)
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 - 2 q^{3} + 16 q^{5} - 23 q^{9}+O(q^{10}) $

$ q - 2 q^{3} + 16 q^{5} - 23 q^{9} - 24 q^{11} + 68 q^{13} - 32 q^{15} - 54 q^{17} - 46 q^{19} - 176 q^{23} + 131 q^{25} + 100 q^{27} - 174 q^{29} - 116 q^{31} + 48 q^{33} + 74 q^{37} - 136 q^{39} + 10 q^{41} + 480 q^{43} - 368 q^{45} - 572 q^{47} + 108 q^{51} - 162 q^{53} - 384 q^{55} + 92 q^{57} - 86 q^{59} + 904 q^{61} + 1088 q^{65} - 660 q^{67} + 352 q^{69} - 1024 q^{71} - 770 q^{73} - 262 q^{75} + 904 q^{79} + 421 q^{81} + 682 q^{83} - 864 q^{85} + 348 q^{87} + 102 q^{89} + 232 q^{93} - 736 q^{95} + 218 q^{97} + 552 q^{99}+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

−2.00000

16.0000

−23.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$1$
$7$	$-1$

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	784.4.a.i		1
4.b	odd	2	1		392.4.a.c		1
7.b	odd	2	1		112.4.a.d		1
21.c	even	2	1		1008.4.a.u		1
28.d	even	2	1		56.4.a.a	✓	1
28.f	even	6	2		392.4.i.e		2
28.g	odd	6	2		392.4.i.d		2
56.e	even	2	1		448.4.a.l		1
56.h	odd	2	1		448.4.a.h		1
84.h	odd	2	1		504.4.a.g		1
140.c	even	2	1		1400.4.a.f		1
140.j	odd	4	2		1400.4.g.f		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
56.4.a.a	✓	1	28.d	even	2	1
112.4.a.d		1	7.b	odd	2	1
392.4.a.c		1	4.b	odd	2	1
392.4.i.d		2	28.g	odd	6	2
392.4.i.e		2	28.f	even	6	2
448.4.a.h		1	56.h	odd	2	1
448.4.a.l		1	56.e	even	2	1
504.4.a.g		1	84.h	odd	2	1
784.4.a.i		1	1.a	even	1	1	trivial
1008.4.a.u		1	21.c	even	2	1
1400.4.a.f		1	140.c	even	2	1
1400.4.g.f		2	140.j	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(784))$:

$ T_{3} + 2 $

$ T_{5} - 16 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 2 $ T + 2
$5$	$ T - 16 $ T - 16
$7$	$ T $ T
$11$	$ T + 24 $ T + 24
$13$	$ T - 68 $ T - 68
$17$	$ T + 54 $ T + 54
$19$	$ T + 46 $ T + 46
$23$	$ T + 176 $ T + 176
$29$	$ T + 174 $ T + 174
$31$	$ T + 116 $ T + 116
$37$	$ T - 74 $ T - 74
$41$	$ T - 10 $ T - 10
$43$	$ T - 480 $ T - 480
$47$	$ T + 572 $ T + 572
$53$	$ T + 162 $ T + 162
$59$	$ T + 86 $ T + 86
$61$	$ T - 904 $ T - 904
$67$	$ T + 660 $ T + 660
$71$	$ T + 1024 $ T + 1024
$73$	$ T + 770 $ T + 770
$79$	$ T - 904 $ T - 904
$83$	$ T - 682 $ T - 682
$89$	$ T - 102 $ T - 102
$97$	$ T - 218 $ T - 218
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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	784.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