LMFDB - Newform orbit 1872.4.a.e

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1872,4,Mod(1,1872)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1872, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1872.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$1872 = 2^{4} \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1872.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:	$110.451575531$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 78)
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 - 6 q^{5} - 20 q^{7} + 24 q^{11} + 13 q^{13} + 30 q^{17} + 16 q^{19} - 72 q^{23} - 89 q^{25} + 282 q^{29} - 164 q^{31} + 120 q^{35} + 110 q^{37} + 126 q^{41} - 164 q^{43} - 204 q^{47} + 57 q^{49} + 738 q^{53}+ \cdots - 1726 q^{97}+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

−6.00000

−20.0000

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$13$	$-1$

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	1872.4.a.e		1
3.b	odd	2	1		624.4.a.i		1
4.b	odd	2	1		234.4.a.b		1
12.b	even	2	1		78.4.a.e	✓	1
24.f	even	2	1		2496.4.a.k		1
24.h	odd	2	1		2496.4.a.b		1
60.h	even	2	1		1950.4.a.c		1
156.h	even	2	1		1014.4.a.b		1
156.l	odd	4	2		1014.4.b.c		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
78.4.a.e	✓	1	12.b	even	2	1
234.4.a.b		1	4.b	odd	2	1
624.4.a.i		1	3.b	odd	2	1
1014.4.a.b		1	156.h	even	2	1
1014.4.b.c		2	156.l	odd	4	2
1872.4.a.e		1	1.a	even	1	1	trivial
1950.4.a.c		1	60.h	even	2	1
2496.4.a.b		1	24.h	odd	2	1
2496.4.a.k		1	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1872))$ :

T_{5} + 6

T_{7} + 20

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T$ T
$5$	$T + 6$ T + 6
$7$	$T + 20$ T + 20
$11$	$T - 24$ T - 24
$13$	$T - 13$ T - 13
$17$	$T - 30$ T - 30
$19$	$T - 16$ T - 16
$23$	$T + 72$ T + 72
$29$	$T - 282$ T - 282
$31$	$T + 164$ T + 164
$37$	$T - 110$ T - 110
$41$	$T - 126$ T - 126
$43$	$T + 164$ T + 164
$47$	$T + 204$ T + 204
$53$	$T - 738$ T - 738
$59$	$T - 120$ T - 120
$61$	$T - 614$ T - 614
$67$	$T + 848$ T + 848
$71$	$T - 132$ T - 132
$73$	$T - 218$ T - 218
$79$	$T - 1096$ T - 1096
$83$	$T - 552$ T - 552
$89$	$T + 210$ T + 210
$97$	$T + 1726$ T + 1726
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