LMFDB - Newform orbit 1638.2.a.c

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(1,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, 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("1638.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.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:	$13.0794958511$
Analytic rank:	$0$
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} - 2 q^{5} - q^{7} - q^{8}+O(q^{10}) $

$ q - q^{2} + q^{4} - 2 q^{5} - q^{7} - q^{8} + 2 q^{10} - 4 q^{11} - q^{13} + q^{14} + q^{16} + 6 q^{17} - 2 q^{20} + 4 q^{22} - 8 q^{23} - q^{25} + q^{26} - q^{28} + 10 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} + 2 q^{35} + 6 q^{37} + 2 q^{40} + 6 q^{41} + 4 q^{43} - 4 q^{44} + 8 q^{46} + 8 q^{47} + q^{49} + q^{50} - q^{52} - 6 q^{53} + 8 q^{55} + q^{56} - 10 q^{58} - 8 q^{59} + 10 q^{61} + 8 q^{62} + q^{64} + 2 q^{65} + 4 q^{67} + 6 q^{68} - 2 q^{70} + 8 q^{71} + 2 q^{73} - 6 q^{74} + 4 q^{77} + 8 q^{79} - 2 q^{80} - 6 q^{82} - 12 q^{85} - 4 q^{86} + 4 q^{88} - 18 q^{89} + q^{91} - 8 q^{92} - 8 q^{94} + 2 q^{97} - q^{98}+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

−2.00000

−1.00000

2.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$1$
$3$	$-1$
$7$	$1$
$13$	$1$

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	1638.2.a.c		1
3.b	odd	2	1		182.2.a.c	✓	1
12.b	even	2	1		1456.2.a.i		1
15.d	odd	2	1		4550.2.a.g		1
21.c	even	2	1		1274.2.a.l		1
21.g	even	6	2		1274.2.f.g		2
21.h	odd	6	2		1274.2.f.f		2
24.f	even	2	1		5824.2.a.m		1
24.h	odd	2	1		5824.2.a.l		1
39.d	odd	2	1		2366.2.a.d		1
39.f	even	4	2		2366.2.d.d		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
182.2.a.c	✓	1	3.b	odd	2	1
1274.2.a.l		1	21.c	even	2	1
1274.2.f.f		2	21.h	odd	6	2
1274.2.f.g		2	21.g	even	6	2
1456.2.a.i		1	12.b	even	2	1
1638.2.a.c		1	1.a	even	1	1	trivial
2366.2.a.d		1	39.d	odd	2	1
2366.2.d.d		2	39.f	even	4	2
4550.2.a.g		1	15.d	odd	2	1
5824.2.a.l		1	24.h	odd	2	1
5824.2.a.m		1	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(1638))$:

$ T_{5} + 2 $

$ T_{11} + 4 $

$ T_{17} - 6 $

$ T_{19} $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 1 $ T + 1
$3$	$ T $ T
$5$	$ T + 2 $ T + 2
$7$	$ 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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Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.a (trivial)

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