LMFDB - Newform orbit 225.2.a.d

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(1,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

−2.00000

5.00000

Atkin-Lehner signs

$ p $	Sign
$3$	$1$
$5$	$-1$

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by $\Q(\sqrt{-3}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	225.2.a.d	yes	1
3.b	odd	2	1	CM	225.2.a.d	yes	1
4.b	odd	2	1		3600.2.a.b		1
5.b	even	2	1		225.2.a.c	✓	1
5.c	odd	4	2		225.2.b.c		2
12.b	even	2	1		3600.2.a.b		1
15.d	odd	2	1		225.2.a.c	✓	1
15.e	even	4	2		225.2.b.c		2
20.d	odd	2	1		3600.2.a.br		1
20.e	even	4	2		3600.2.f.k		2
60.h	even	2	1		3600.2.a.br		1
60.l	odd	4	2		3600.2.f.k		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
225.2.a.c	✓	1	5.b	even	2	1
225.2.a.c	✓	1	15.d	odd	2	1
225.2.a.d	yes	1	1.a	even	1	1	trivial
225.2.a.d	yes	1	3.b	odd	2	1	CM
225.2.b.c		2	5.c	odd	4	2
225.2.b.c		2	15.e	even	4	2
3600.2.a.b		1	4.b	odd	2	1
3600.2.a.b		1	12.b	even	2	1
3600.2.a.br		1	20.d	odd	2	1
3600.2.a.br		1	60.h	even	2	1
3600.2.f.k		2	20.e	even	4	2
3600.2.f.k		2	60.l	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(225))$:

$ T_{2} $

$ T_{7} - 5 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T - 5 $ T - 5
$11$	$ T $ T
$13$	$ T - 5 $ T - 5
$17$	$ T $ T
$19$	$ T + 1 $ T + 1
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T + 7 $ T + 7
$37$	$ T + 10 $ T + 10
$41$	$ T $ T
$43$	$ T - 5 $ T - 5
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T + 13 $ T + 13
$67$	$ T - 5 $ T - 5
$71$	$ T $ T
$73$	$ T + 10 $ T + 10
$79$	$ T + 4 $ T + 4
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T - 5 $ T - 5
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.a (trivial)

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