LMFDB - Newform orbit 96.3.h.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,3,Mod(17,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("96.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	96.h (of order $2$, degree $1$, not minimal)

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:	$2.61581053786$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q + 3 q^{3} - 2 q^{5} + 10 q^{7} + 9 q^{9}+O(q^{10}) $

$ q + 3 q^{3} - 2 q^{5} + 10 q^{7} + 9 q^{9} - 10 q^{11} - 6 q^{15} + 30 q^{21} - 21 q^{25} + 27 q^{27} - 50 q^{29} - 38 q^{31} - 30 q^{33} - 20 q^{35} - 18 q^{45} + 51 q^{49} + 94 q^{53} + 20 q^{55} - 10 q^{59} + 90 q^{63} + 50 q^{73} - 63 q^{75} - 100 q^{77} + 58 q^{79} + 81 q^{81} + 134 q^{83} - 150 q^{87} - 114 q^{93} - 190 q^{97} - 90 q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$-1$	$-1$

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} $

17.1

3.00000

−2.00000

10.0000

9.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
24.h	odd	2	1	CM by $\Q(\sqrt{-6}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	96.3.h.b		1
3.b	odd	2	1		96.3.h.a		1
4.b	odd	2	1		24.3.h.b	yes	1
8.b	even	2	1		96.3.h.a		1
8.d	odd	2	1		24.3.h.a	✓	1
12.b	even	2	1		24.3.h.a	✓	1
16.e	even	4	2		768.3.e.c		2
16.f	odd	4	2		768.3.e.d		2
24.f	even	2	1		24.3.h.b	yes	1
24.h	odd	2	1	CM	96.3.h.b		1
48.i	odd	4	2		768.3.e.c		2
48.k	even	4	2		768.3.e.d		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
24.3.h.a	✓	1	8.d	odd	2	1
24.3.h.a	✓	1	12.b	even	2	1
24.3.h.b	yes	1	4.b	odd	2	1
24.3.h.b	yes	1	24.f	even	2	1
96.3.h.a		1	3.b	odd	2	1
96.3.h.a		1	8.b	even	2	1
96.3.h.b		1	1.a	even	1	1	trivial
96.3.h.b		1	24.h	odd	2	1	CM
768.3.e.c		2	16.e	even	4	2
768.3.e.c		2	48.i	odd	4	2
768.3.e.d		2	16.f	odd	4	2
768.3.e.d		2	48.k	even	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5} + 2 $ T5 + 2 acting on $S_{3}^{\mathrm{new}}(96, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 3 $ T - 3
$5$	$ T + 2 $ T + 2
$7$	$ T - 10 $ T - 10
$11$	$ T + 10 $ T + 10
$13$	$ T $ T
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T $ T
$29$	$ T + 50 $ T + 50
$31$	$ T + 38 $ T + 38
$37$	$ T $ T
$41$	$ T $ T
$43$	$ T $ T
$47$	$ T $ T
$53$	$ T - 94 $ T - 94
$59$	$ T + 10 $ T + 10
$61$	$ T $ T
$67$	$ T $ T
$71$	$ T $ T
$73$	$ T - 50 $ T - 50
$79$	$ T - 58 $ T - 58
$83$	$ T - 134 $ T - 134
$89$	$ T $ T
$97$	$ T + 190 $ T + 190
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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	96.h (of order \(2\), degree \(1\), not minimal)

\(n\)	\(31\)	\(37\)	\(65\)
\(\chi(n)\)	\(1\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more