LMFDB - Newform orbit 1150.4.a.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
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 - 2 q^{2} - 2 q^{3} + 4 q^{4} + 4 q^{6} - 21 q^{7} - 8 q^{8} - 23 q^{9} + 47 q^{11} - 8 q^{12} - 57 q^{13} + 42 q^{14} + 16 q^{16} + 84 q^{17} + 46 q^{18} - 5 q^{19} + 42 q^{21} - 94 q^{22} - 23 q^{23}+ \cdots - 1081 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

−2.00000

4.00000

−21.0000

−8.00000

−23.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$5$	$ -1 $
$23$	$ +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	1150.4.a.a	✓	1
5.b	even	2	1		1150.4.a.h	yes	1
5.c	odd	4	2		1150.4.b.g		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1150.4.a.a	✓	1	1.a	even	1	1	trivial
1150.4.a.h	yes	1	5.b	even	2	1
1150.4.b.g		2	5.c	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1150))$:

$ T_{3} + 2 $

$ T_{7} + 21 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T + 2 $ T + 2
$5$	$ T $ T
$7$	$ T + 21 $ T + 21
$11$	$ T - 47 $ T - 47
$13$	$ T + 57 $ T + 57
$17$	$ T - 84 $ T - 84
$19$	$ T + 5 $ T + 5
$23$	$ T + 23 $ T + 23
$29$	$ T - 285 $ T - 285
$31$	$ T - 82 $ T - 82
$37$	$ T - 54 $ T - 54
$41$	$ T + 53 $ T + 53
$43$	$ T + 197 $ T + 197
$47$	$ T - 124 $ T - 124
$53$	$ T - 148 $ T - 148
$59$	$ T - 30 $ T - 30
$61$	$ T + 578 $ T + 578
$67$	$ T + 296 $ T + 296
$71$	$ T - 422 $ T - 422
$73$	$ T + 487 $ T + 487
$79$	$ T + 405 $ T + 405
$83$	$ T + 397 $ T + 397
$89$	$ T - 730 $ T - 730
$97$	$ T - 64 $ T - 64
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Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

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