LMFDB - Newform orbit 4550.2.a.g

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4550,2,Mod(1,4550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4550, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4550 = 2 \cdot 5^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4550.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:	$36.3319329197$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
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} + q^{7} - q^{8} - 3 q^{9}+O(q^{10}) $

$ q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} + 4 q^{11} + q^{13} - q^{14} + q^{16} + 6 q^{17} + 3 q^{18} - 4 q^{22} - 8 q^{23} - q^{26} + q^{28} - 10 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} - 3 q^{36} - 6 q^{37} - 6 q^{41} - 4 q^{43} + 4 q^{44} + 8 q^{46} + 8 q^{47} + q^{49} + q^{52} - 6 q^{53} - q^{56} + 10 q^{58} + 8 q^{59} + 10 q^{61} + 8 q^{62} - 3 q^{63} + q^{64} - 4 q^{67} + 6 q^{68} - 8 q^{71} + 3 q^{72} - 2 q^{73} + 6 q^{74} + 4 q^{77} + 8 q^{79} + 9 q^{81} + 6 q^{82} + 4 q^{86} - 4 q^{88} + 18 q^{89} + q^{91} - 8 q^{92} - 8 q^{94} - 2 q^{97} - q^{98} - 12 q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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

1.00000

−1.00000

−3.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$1$
$5$	$1$
$7$	$-1$
$13$	$-1$

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	4550.2.a.g		1
5.b	even	2	1		182.2.a.c	✓	1
15.d	odd	2	1		1638.2.a.c		1
20.d	odd	2	1		1456.2.a.i		1
35.c	odd	2	1		1274.2.a.l		1
35.i	odd	6	2		1274.2.f.g		2
35.j	even	6	2		1274.2.f.f		2
40.e	odd	2	1		5824.2.a.m		1
40.f	even	2	1		5824.2.a.l		1
65.d	even	2	1		2366.2.a.d		1
65.g	odd	4	2		2366.2.d.d		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
182.2.a.c	✓	1	5.b	even	2	1
1274.2.a.l		1	35.c	odd	2	1
1274.2.f.f		2	35.j	even	6	2
1274.2.f.g		2	35.i	odd	6	2
1456.2.a.i		1	20.d	odd	2	1
1638.2.a.c		1	15.d	odd	2	1
2366.2.a.d		1	65.d	even	2	1
2366.2.d.d		2	65.g	odd	4	2
4550.2.a.g		1	1.a	even	1	1	trivial
5824.2.a.l		1	40.f	even	2	1
5824.2.a.m		1	40.e	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(4550))$:

$ T_{3} $

$ T_{11} - 4 $

$ T_{17} - 6 $

$ T_{19} $

$ T_{23} + 8 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 1 $ T + 1
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T - 1 $ T - 1
$11$	$ T - 4 $ T - 4
$13$	$ T - 1 $ T - 1
$17$	$ T - 6 $ T - 6
$19$	$ T $ T
$23$	$ T + 8 $ T + 8
$29$	$ T + 10 $ T + 10
$31$	$ T + 8 $ T + 8
$37$	$ T + 6 $ T + 6
$41$	$ T + 6 $ T + 6
$43$	$ T + 4 $ T + 4
$47$	$ T - 8 $ T - 8
$53$	$ T + 6 $ T + 6
$59$	$ T - 8 $ T - 8
$61$	$ T - 10 $ T - 10
$67$	$ T + 4 $ T + 4
$71$	$ T + 8 $ T + 8
$73$	$ T + 2 $ T + 2
$79$	$ T - 8 $ T - 8
$83$	$ T $ T
$89$	$ T - 18 $ T - 18
$97$	$ T + 2 $ T + 2
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 4550 = 2 \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4550.a (trivial)

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