LMFDB - Newform orbit 1650.2.a.r

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1650,2,Mod(1,1650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1650, 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("1650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1650.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:	$13.1753163335$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
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^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{11} + q^{12} - 2 q^{13} + q^{16} + 2 q^{17} + q^{18} + 8 q^{19} + q^{22} - 4 q^{23} + q^{24} - 2 q^{26} + q^{27} + 2 q^{29} + 8 q^{31}+ \cdots + q^{99}+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

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$3$	$ -1 $
$5$	$ +1 $
$11$	$ -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	1650.2.a.r		1
3.b	odd	2	1		4950.2.a.k		1
5.b	even	2	1		330.2.a.a	✓	1
5.c	odd	4	2		1650.2.c.l		2
15.d	odd	2	1		990.2.a.j		1
15.e	even	4	2		4950.2.c.g		2
20.d	odd	2	1		2640.2.a.n		1
55.d	odd	2	1		3630.2.a.n		1
60.h	even	2	1		7920.2.a.bb		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
330.2.a.a	✓	1	5.b	even	2	1
990.2.a.j		1	15.d	odd	2	1
1650.2.a.r		1	1.a	even	1	1	trivial
1650.2.c.l		2	5.c	odd	4	2
2640.2.a.n		1	20.d	odd	2	1
3630.2.a.n		1	55.d	odd	2	1
4950.2.a.k		1	3.b	odd	2	1
4950.2.c.g		2	15.e	even	4	2
7920.2.a.bb		1	60.h	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(1650))$:

$ T_{7} $

$ T_{13} + 2 $

$ T_{17} - 2 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 1 $ T - 1
$3$	$ T - 1 $ T - 1
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T - 1 $ T - 1
$13$	$ T + 2 $ T + 2
$17$	$ T - 2 $ T - 2
$19$	$ T - 8 $ T - 8
$23$	$ T + 4 $ T + 4
$29$	$ T - 2 $ T - 2
$31$	$ T - 8 $ T - 8
$37$	$ T - 2 $ T - 2
$41$	$ T - 6 $ T - 6
$43$	$ T + 8 $ T + 8
$47$	$ T - 4 $ T - 4
$53$	$ T + 2 $ T + 2
$59$	$ T - 4 $ T - 4
$61$	$ T + 6 $ T + 6
$67$	$ T - 12 $ T - 12
$71$	$ T + 12 $ T + 12
$73$	$ T + 2 $ T + 2
$79$	$ T $ T
$83$	$ T + 4 $ T + 4
$89$	$ T + 6 $ T + 6
$97$	$ T - 14 $ T - 14
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Elliptic curves over $\Q$
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Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.a (trivial)

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