LMFDB - Newform orbit 2240.2.a.r

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(1,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, 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("2240.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.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:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
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} - q^{5} - q^{7} - 2 q^{9}+O(q^{10}) $

$ q + q^{3} - q^{5} - q^{7} - 2 q^{9} + 3 q^{11} + q^{13} - q^{15} - 3 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + q^{25} - 5 q^{27} + 9 q^{29} - 8 q^{31} + 3 q^{33} + q^{35} + 10 q^{37} + q^{39} + 2 q^{43} + 2 q^{45} + 3 q^{47} + q^{49} - 3 q^{51} - 3 q^{55} + 2 q^{57} + 12 q^{59} - 8 q^{61} + 2 q^{63} - q^{65} + 8 q^{67} + 6 q^{69} + 14 q^{73} + q^{75} - 3 q^{77} - 5 q^{79} + q^{81} - 12 q^{83} + 3 q^{85} + 9 q^{87} + 12 q^{89} - q^{91} - 8 q^{93} - 2 q^{95} + 17 q^{97} - 6 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

−1.00000

−2.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$5$	$ +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	2240.2.a.r		1
4.b	odd	2	1		2240.2.a.g		1
8.b	even	2	1		560.2.a.c		1
8.d	odd	2	1		140.2.a.a	✓	1
24.f	even	2	1		1260.2.a.c		1
24.h	odd	2	1		5040.2.a.h		1
40.e	odd	2	1		700.2.a.d		1
40.f	even	2	1		2800.2.a.y		1
40.i	odd	4	2		2800.2.g.j		2
40.k	even	4	2		700.2.e.c		2
56.e	even	2	1		980.2.a.c		1
56.h	odd	2	1		3920.2.a.u		1
56.k	odd	6	2		980.2.i.d		2
56.m	even	6	2		980.2.i.h		2
120.m	even	2	1		6300.2.a.d		1
120.q	odd	4	2		6300.2.k.c		2
168.e	odd	2	1		8820.2.a.r		1
280.n	even	2	1		4900.2.a.p		1
280.y	odd	4	2		4900.2.e.l		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.2.a.a	✓	1	8.d	odd	2	1
560.2.a.c		1	8.b	even	2	1
700.2.a.d		1	40.e	odd	2	1
700.2.e.c		2	40.k	even	4	2
980.2.a.c		1	56.e	even	2	1
980.2.i.d		2	56.k	odd	6	2
980.2.i.h		2	56.m	even	6	2
1260.2.a.c		1	24.f	even	2	1
2240.2.a.g		1	4.b	odd	2	1
2240.2.a.r		1	1.a	even	1	1	trivial
2800.2.a.y		1	40.f	even	2	1
2800.2.g.j		2	40.i	odd	4	2
3920.2.a.u		1	56.h	odd	2	1
4900.2.a.p		1	280.n	even	2	1
4900.2.e.l		2	280.y	odd	4	2
5040.2.a.h		1	24.h	odd	2	1
6300.2.a.d		1	120.m	even	2	1
6300.2.k.c		2	120.q	odd	4	2
8820.2.a.r		1	168.e	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(2240))$:

$ T_{3} - 1 $

$ T_{11} - 3 $

$ T_{13} - 1 $

$ T_{19} - 2 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 1 $ T - 1
$5$	$ T + 1 $ T + 1
$7$	$ T + 1 $ T + 1
$11$	$ T - 3 $ T - 3
$13$	$ T - 1 $ T - 1
$17$	$ T + 3 $ T + 3
$19$	$ T - 2 $ T - 2
$23$	$ T - 6 $ T - 6
$29$	$ T - 9 $ T - 9
$31$	$ T + 8 $ T + 8
$37$	$ T - 10 $ T - 10
$41$	$ T $ T
$43$	$ T - 2 $ T - 2
$47$	$ T - 3 $ T - 3
$53$	$ T $ T
$59$	$ T - 12 $ T - 12
$61$	$ T + 8 $ T + 8
$67$	$ T - 8 $ T - 8
$71$	$ T $ T
$73$	$ T - 14 $ T - 14
$79$	$ T + 5 $ T + 5
$83$	$ T + 12 $ T + 12
$89$	$ T - 12 $ T - 12
$97$	$ T - 17 $ T - 17
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Overview	Random
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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:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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