LMFDB - Newform orbit 189.2.a.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(1,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("189.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$189 = 3^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	189.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:	$1.50917259820$
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 - 2 q^{2} + 2 q^{4} - q^{5} - q^{7} + 2 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 4 q^{16} + 3 q^{17} - 8 q^{19} - 2 q^{20} + 8 q^{22} - 6 q^{23} - 4 q^{25} + 4 q^{26} - 2 q^{28} - 4 q^{29} + 6 q^{31}+ \cdots - 2 q^{98}+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

−2.00000

2.00000

−1.00000

2.00000

Atkin-Lehner signs

$p$	Sign
$3$	$+1$
$7$	$+1$

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	189.2.a.a	✓	1
3.b	odd	2	1		189.2.a.d	yes	1
4.b	odd	2	1		3024.2.a.l		1
5.b	even	2	1		4725.2.a.s		1
7.b	odd	2	1		1323.2.a.b		1
9.c	even	3	2		567.2.f.h		2
9.d	odd	6	2		567.2.f.a		2
12.b	even	2	1		3024.2.a.u		1
15.d	odd	2	1		4725.2.a.c		1
21.c	even	2	1		1323.2.a.r		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
189.2.a.a	✓	1	1.a	even	1	1	trivial
189.2.a.d	yes	1	3.b	odd	2	1
567.2.f.a		2	9.d	odd	6	2
567.2.f.h		2	9.c	even	3	2
1323.2.a.b		1	7.b	odd	2	1
1323.2.a.r		1	21.c	even	2	1
3024.2.a.l		1	4.b	odd	2	1
3024.2.a.u		1	12.b	even	2	1
4725.2.a.c		1	15.d	odd	2	1
4725.2.a.s		1	5.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(189))$ :

T_{2} + 2

T_{5} + 1

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$ T + 2
$3$	$T$ T
$5$	$T + 1$ T + 1
$7$	$T + 1$ T + 1
$11$	$T + 4$ T + 4
$13$	$T + 2$ T + 2
$17$	$T - 3$ T - 3
$19$	$T + 8$ T + 8
$23$	$T + 6$ T + 6
$29$	$T + 4$ T + 4
$31$	$T - 6$ T - 6
$37$	$T + 3$ T + 3
$41$	$T - 1$ T - 1
$43$	$T - 11$ T - 11
$47$	$T - 9$ T - 9
$53$	$T - 6$ T - 6
$59$	$T + 15$ T + 15
$61$	$T - 4$ T - 4
$67$	$T + 8$ T + 8
$71$	$T + 12$ T + 12
$73$	$T - 6$ T - 6
$79$	$T + 1$ T + 1
$83$	$T + 9$ T + 9
$89$	$T - 2$ T - 2
$97$	$T - 12$ T - 12
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