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)

f(q)

=

q - 10 q^{7} + 46 q^{11} + 34 q^{13} + 66 q^{17} + 104 q^{19} + 164 q^{23} - 224 q^{29} - 72 q^{31} + 22 q^{37} - 194 q^{41} - 108 q^{43} - 480 q^{47} - 243 q^{49} + 286 q^{53} - 426 q^{59} + 698 q^{61}+ \cdots + 1384 q^{97}+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

−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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