LMFDB - Newform orbit 1800.4.a.j

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,4,Mod(1,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1800.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1800.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:	$106.203438010$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
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)

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

−10.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$3$	$ -1 $
$5$	$ -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	1800.4.a.j		1
3.b	odd	2	1		600.4.a.b		1
5.b	even	2	1		1800.4.a.y		1
5.c	odd	4	2		360.4.f.c		2
12.b	even	2	1		1200.4.a.bh		1
15.d	odd	2	1		600.4.a.o		1
15.e	even	4	2		120.4.f.a	✓	2
20.e	even	4	2		720.4.f.g		2
60.h	even	2	1		1200.4.a.f		1
60.l	odd	4	2		240.4.f.b		2
120.q	odd	4	2		960.4.f.g		2
120.w	even	4	2		960.4.f.l		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
120.4.f.a	✓	2	15.e	even	4	2
240.4.f.b		2	60.l	odd	4	2
360.4.f.c		2	5.c	odd	4	2
600.4.a.b		1	3.b	odd	2	1
600.4.a.o		1	15.d	odd	2	1
720.4.f.g		2	20.e	even	4	2
960.4.f.g		2	120.q	odd	4	2
960.4.f.l		2	120.w	even	4	2
1200.4.a.f		1	60.h	even	2	1
1200.4.a.bh		1	12.b	even	2	1
1800.4.a.j		1	1.a	even	1	1	trivial
1800.4.a.y		1	5.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1800))$:

$ T_{7} + 10 $

$ T_{11} - 46 $

$ T_{17} - 66 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T + 10 $ T + 10
$11$	$ T - 46 $ T - 46
$13$	$ T - 34 $ T - 34
$17$	$ T - 66 $ T - 66
$19$	$ T - 104 $ T - 104
$23$	$ T - 164 $ T - 164
$29$	$ T + 224 $ T + 224
$31$	$ T + 72 $ T + 72
$37$	$ T - 22 $ T - 22
$41$	$ T + 194 $ T + 194
$43$	$ T + 108 $ T + 108
$47$	$ T + 480 $ T + 480
$53$	$ T - 286 $ T - 286
$59$	$ T + 426 $ T + 426
$61$	$ T - 698 $ T - 698
$67$	$ T + 328 $ T + 328
$71$	$ T + 188 $ T + 188
$73$	$ T - 740 $ T - 740
$79$	$ T - 1168 $ T - 1168
$83$	$ T - 412 $ T - 412
$89$	$ T + 1206 $ T + 1206
$97$	$ T - 1384 $ T - 1384
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Overview	Random
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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1800.a (trivial)

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