LMFDB - Newform orbit 200.4.a.f

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,Mod(1,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, 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("200.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$200 = 2^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	200.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:	$11.8003820011$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
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 + q^{3} - 6 q^{7} - 26 q^{9} - 19 q^{11} + 12 q^{13} - 75 q^{17} - 91 q^{19} - 6 q^{21} + 174 q^{23} - 53 q^{27} - 272 q^{29} - 230 q^{31} - 19 q^{33} - 182 q^{37} + 12 q^{39} + 117 q^{41} + 372 q^{43}+ \cdots + 494 q^{99}+O(q^{100})

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

−6.00000

−26.0000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$5$	$-1$

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	200.4.a.f	yes	1
3.b	odd	2	1		1800.4.a.l		1
4.b	odd	2	1		400.4.a.j		1
5.b	even	2	1		200.4.a.e	✓	1
5.c	odd	4	2		200.4.c.g		2
8.b	even	2	1		1600.4.a.w		1
8.d	odd	2	1		1600.4.a.be		1
15.d	odd	2	1		1800.4.a.w		1
15.e	even	4	2		1800.4.f.p		2
20.d	odd	2	1		400.4.a.k		1
20.e	even	4	2		400.4.c.m		2
40.e	odd	2	1		1600.4.a.v		1
40.f	even	2	1		1600.4.a.bf		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
200.4.a.e	✓	1	5.b	even	2	1
200.4.a.f	yes	1	1.a	even	1	1	trivial
200.4.c.g		2	5.c	odd	4	2
400.4.a.j		1	4.b	odd	2	1
400.4.a.k		1	20.d	odd	2	1
400.4.c.m		2	20.e	even	4	2
1600.4.a.v		1	40.e	odd	2	1
1600.4.a.w		1	8.b	even	2	1
1600.4.a.be		1	8.d	odd	2	1
1600.4.a.bf		1	40.f	even	2	1
1800.4.a.l		1	3.b	odd	2	1
1800.4.a.w		1	15.d	odd	2	1
1800.4.f.p		2	15.e	even	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} - 1$ T3 - 1 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(200))$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T - 1$ T - 1
$5$	$T$ T
$7$	$T + 6$ T + 6
$11$	$T + 19$ T + 19
$13$	$T - 12$ T - 12
$17$	$T + 75$ T + 75
$19$	$T + 91$ T + 91
$23$	$T - 174$ T - 174
$29$	$T + 272$ T + 272
$31$	$T + 230$ T + 230
$37$	$T + 182$ T + 182
$41$	$T - 117$ T - 117
$43$	$T - 372$ T - 372
$47$	$T + 52$ T + 52
$53$	$T + 402$ T + 402
$59$	$T - 312$ T - 312
$61$	$T - 170$ T - 170
$67$	$T - 763$ T - 763
$71$	$T + 52$ T + 52
$73$	$T + 981$ T + 981
$79$	$T - 1054$ T - 1054
$83$	$T - 351$ T - 351
$89$	$T - 799$ T - 799
$97$	$T - 962$ T - 962
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 $\F_{q}$

$n$ :		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