LMFDB - Newform orbit 2496.2.a.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2496,2,Mod(1,2496)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2496, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2496.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2496 = 2^{6} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2496.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:	$19.9306603445$
Analytic rank:	$0$
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 - q^{3} - 2 q^{5} - 4 q^{7} + q^{9}+O(q^{10}) $

$ q - q^{3} - 2 q^{5} - 4 q^{7} + q^{9} - 4 q^{11} - q^{13} + 2 q^{15} + 2 q^{17} - 8 q^{19} + 4 q^{21} - q^{25} - q^{27} - 6 q^{29} + 4 q^{31} + 4 q^{33} + 8 q^{35} + 2 q^{37} + q^{39} - 10 q^{41} + 4 q^{43} - 2 q^{45} - 8 q^{47} + 9 q^{49} - 2 q^{51} + 10 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} - 4 q^{63} + 2 q^{65} - 16 q^{67} + 8 q^{71} + 2 q^{73} + q^{75} + 16 q^{77} - 8 q^{79} + q^{81} + 12 q^{83} - 4 q^{85} + 6 q^{87} + 14 q^{89} + 4 q^{91} - 4 q^{93} + 16 q^{95} + 10 q^{97} - 4 q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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

−2.00000

−4.00000

1.00000

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	2496.2.a.b		1
3.b	odd	2	1		7488.2.a.bk		1
4.b	odd	2	1		2496.2.a.t		1
8.b	even	2	1		624.2.a.h		1
8.d	odd	2	1		78.2.a.a	✓	1
12.b	even	2	1		7488.2.a.bz		1
24.f	even	2	1		234.2.a.c		1
24.h	odd	2	1		1872.2.a.c		1
40.e	odd	2	1		1950.2.a.w		1
40.k	even	4	2		1950.2.e.i		2
56.e	even	2	1		3822.2.a.j		1
72.l	even	6	2		2106.2.e.j		2
72.p	odd	6	2		2106.2.e.q		2
88.g	even	2	1		9438.2.a.t		1
104.e	even	2	1		8112.2.a.v		1
104.h	odd	2	1		1014.2.a.d		1
104.m	even	4	2		1014.2.b.b		2
104.n	odd	6	2		1014.2.e.f		2
104.p	odd	6	2		1014.2.e.c		2
104.u	even	12	4		1014.2.i.d		4
120.m	even	2	1		5850.2.a.d		1
120.q	odd	4	2		5850.2.e.bb		2
312.h	even	2	1		3042.2.a.f		1
312.w	odd	4	2		3042.2.b.g		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
78.2.a.a	✓	1	8.d	odd	2	1
234.2.a.c		1	24.f	even	2	1
624.2.a.h		1	8.b	even	2	1
1014.2.a.d		1	104.h	odd	2	1
1014.2.b.b		2	104.m	even	4	2
1014.2.e.c		2	104.p	odd	6	2
1014.2.e.f		2	104.n	odd	6	2
1014.2.i.d		4	104.u	even	12	4
1872.2.a.c		1	24.h	odd	2	1
1950.2.a.w		1	40.e	odd	2	1
1950.2.e.i		2	40.k	even	4	2
2106.2.e.j		2	72.l	even	6	2
2106.2.e.q		2	72.p	odd	6	2
2496.2.a.b		1	1.a	even	1	1	trivial
2496.2.a.t		1	4.b	odd	2	1
3042.2.a.f		1	312.h	even	2	1
3042.2.b.g		2	312.w	odd	4	2
3822.2.a.j		1	56.e	even	2	1
5850.2.a.d		1	120.m	even	2	1
5850.2.e.bb		2	120.q	odd	4	2
7488.2.a.bk		1	3.b	odd	2	1
7488.2.a.bz		1	12.b	even	2	1
8112.2.a.v		1	104.e	even	2	1
9438.2.a.t		1	88.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(2496))$:

$ T_{5} + 2 $

$ T_{7} + 4 $

$ T_{11} + 4 $

$ T_{17} - 2 $

$ T_{19} + 8 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 1 $ T + 1
$5$	$ T + 2 $ T + 2
$7$	$ T + 4 $ T + 4
$11$	$ T + 4 $ T + 4
$13$	$ T + 1 $ T + 1
$17$	$ T - 2 $ T - 2
$19$	$ T + 8 $ T + 8
$23$	$ T $ T
$29$	$ T + 6 $ T + 6
$31$	$ T - 4 $ T - 4
$37$	$ T - 2 $ T - 2
$41$	$ T + 10 $ T + 10
$43$	$ T - 4 $ T - 4
$47$	$ T + 8 $ T + 8
$53$	$ T - 10 $ T - 10
$59$	$ T - 4 $ T - 4
$61$	$ T - 2 $ T - 2
$67$	$ T + 16 $ T + 16
$71$	$ T - 8 $ T - 8
$73$	$ T - 2 $ T - 2
$79$	$ T + 8 $ T + 8
$83$	$ T - 12 $ T - 12
$89$	$ T - 14 $ T - 14
$97$	$ T - 10 $ T - 10
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:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2496.a (trivial)

\(n\):		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