LMFDB - Newform orbit 4050.2.a.v

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4050,2,Mod(1,4050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4050, 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("4050.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4050 = 2 \cdot 3^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4050.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:	$32.3394128186$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
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^{4} - 2 q^{7} + q^{8} + 3 q^{11} - 2 q^{13} - 2 q^{14} + q^{16} - 3 q^{17} - q^{19} + 3 q^{22} - 6 q^{23} - 2 q^{26} - 2 q^{28} - 6 q^{29} - 4 q^{31} + q^{32} - 3 q^{34} + 4 q^{37}+ \cdots - 3 q^{98}+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

−2.00000

1.00000

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	4050.2.a.v		1
3.b	odd	2	1		4050.2.a.c		1
5.b	even	2	1		162.2.a.b		1
5.c	odd	4	2		4050.2.c.r		2
9.c	even	3	2		1350.2.e.c		2
9.d	odd	6	2		450.2.e.i		2
15.d	odd	2	1		162.2.a.c		1
15.e	even	4	2		4050.2.c.c		2
20.d	odd	2	1		1296.2.a.f		1
35.c	odd	2	1		7938.2.a.i		1
40.e	odd	2	1		5184.2.a.p		1
40.f	even	2	1		5184.2.a.q		1
45.h	odd	6	2		18.2.c.a	✓	2
45.j	even	6	2		54.2.c.a		2
45.k	odd	12	4		1350.2.j.a		4
45.l	even	12	4		450.2.j.e		4
60.h	even	2	1		1296.2.a.g		1
105.g	even	2	1		7938.2.a.x		1
120.i	odd	2	1		5184.2.a.r		1
120.m	even	2	1		5184.2.a.o		1
180.n	even	6	2		144.2.i.c		2
180.p	odd	6	2		432.2.i.b		2
315.q	odd	6	2		2646.2.e.c		2
315.r	even	6	2		2646.2.e.b		2
315.u	even	6	2		882.2.h.b		2
315.v	odd	6	2		882.2.h.c		2
315.z	even	6	2		882.2.f.d		2
315.bg	odd	6	2		2646.2.f.g		2
315.bn	odd	6	2		2646.2.h.i		2
315.bo	even	6	2		2646.2.h.h		2
315.bq	even	6	2		882.2.e.g		2
315.br	odd	6	2		882.2.e.i		2
360.z	odd	6	2		1728.2.i.f		2
360.bd	even	6	2		576.2.i.a		2
360.bh	odd	6	2		576.2.i.g		2
360.bk	even	6	2		1728.2.i.e		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
18.2.c.a	✓	2	45.h	odd	6	2
54.2.c.a		2	45.j	even	6	2
144.2.i.c		2	180.n	even	6	2
162.2.a.b		1	5.b	even	2	1
162.2.a.c		1	15.d	odd	2	1
432.2.i.b		2	180.p	odd	6	2
450.2.e.i		2	9.d	odd	6	2
450.2.j.e		4	45.l	even	12	4
576.2.i.a		2	360.bd	even	6	2
576.2.i.g		2	360.bh	odd	6	2
882.2.e.g		2	315.bq	even	6	2
882.2.e.i		2	315.br	odd	6	2
882.2.f.d		2	315.z	even	6	2
882.2.h.b		2	315.u	even	6	2
882.2.h.c		2	315.v	odd	6	2
1296.2.a.f		1	20.d	odd	2	1
1296.2.a.g		1	60.h	even	2	1
1350.2.e.c		2	9.c	even	3	2
1350.2.j.a		4	45.k	odd	12	4
1728.2.i.e		2	360.bk	even	6	2
1728.2.i.f		2	360.z	odd	6	2
2646.2.e.b		2	315.r	even	6	2
2646.2.e.c		2	315.q	odd	6	2
2646.2.f.g		2	315.bg	odd	6	2
2646.2.h.h		2	315.bo	even	6	2
2646.2.h.i		2	315.bn	odd	6	2
4050.2.a.c		1	3.b	odd	2	1
4050.2.a.v		1	1.a	even	1	1	trivial
4050.2.c.c		2	15.e	even	4	2
4050.2.c.r		2	5.c	odd	4	2
5184.2.a.o		1	120.m	even	2	1
5184.2.a.p		1	40.e	odd	2	1
5184.2.a.q		1	40.f	even	2	1
5184.2.a.r		1	120.i	odd	2	1
7938.2.a.i		1	35.c	odd	2	1
7938.2.a.x		1	105.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(4050))$:

$ T_{7} + 2 $

$ T_{11} - 3 $

$ T_{13} + 2 $

$ T_{17} + 3 $

$ T_{23} + 6 $

$ T_{41} + 9 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 1 $ T - 1
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T + 2 $ T + 2
$11$	$ T - 3 $ T - 3
$13$	$ T + 2 $ T + 2
$17$	$ T + 3 $ T + 3
$19$	$ T + 1 $ T + 1
$23$	$ T + 6 $ T + 6
$29$	$ T + 6 $ T + 6
$31$	$ T + 4 $ T + 4
$37$	$ T - 4 $ T - 4
$41$	$ T + 9 $ T + 9
$43$	$ T - 1 $ T - 1
$47$	$ T + 6 $ T + 6
$53$	$ T - 12 $ T - 12
$59$	$ T + 3 $ T + 3
$61$	$ T - 8 $ T - 8
$67$	$ T + 5 $ T + 5
$71$	$ T - 12 $ T - 12
$73$	$ T + 11 $ T + 11
$79$	$ T + 4 $ T + 4
$83$	$ T - 12 $ T - 12
$89$	$ T + 6 $ T + 6
$97$	$ T + 5 $ T + 5
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Elliptic curves over $\Q$
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Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4050 = 2 \cdot 3^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4050.a (trivial)

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