LMFDB - Newform orbit 3330.2.a.l

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3330,2,Mod(1,3330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3330, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3330.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3330.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:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 1110)
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^{2} + q^{4} + q^{5} + 4 q^{7} - q^{8} - q^{10} + 2 q^{11} + 2 q^{13} - 4 q^{14} + q^{16} + 2 q^{17} + 2 q^{19} + q^{20} - 2 q^{22} + q^{25} - 2 q^{26} + 4 q^{28} - 2 q^{29} + 4 q^{31} - q^{32}+ \cdots - 9 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

−1.00000

1.00000

4.00000

−1.00000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$
$5$	$-1$
$37$	$-1$

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	3330.2.a.l		1
3.b	odd	2	1		1110.2.a.o	✓	1
12.b	even	2	1		8880.2.a.b		1
15.d	odd	2	1		5550.2.a.b		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1110.2.a.o	✓	1	3.b	odd	2	1
3330.2.a.l		1	1.a	even	1	1	trivial
5550.2.a.b		1	15.d	odd	2	1
8880.2.a.b		1	12.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 $S_{2}^{\mathrm{new}}(\Gamma_0(3330))$ :

T_{7} - 4

T_{11} - 2

T_{13} - 2

T_{17} - 2

Hecke characteristic polynomials

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