LMFDB - Newform orbit 968.2.a.c

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(1,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, 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("968.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$968 = 2^{3} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	968.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:	$7.72951891566$
Analytic rank:	$0$
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 + 3 q^{5} + 4 q^{7} - 3 q^{9} + 3 q^{13} + 3 q^{17} + 4 q^{19} - 8 q^{23} + 4 q^{25} - 5 q^{29} - 4 q^{31} + 12 q^{35} + 11 q^{37} + 7 q^{41} - 12 q^{43} - 9 q^{45} - 8 q^{47} + 9 q^{49} - q^{53} - 4 q^{59}+ \cdots - 13 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

3.00000

4.00000

−3.00000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$11$	$-1$

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	968.2.a.c	yes	1
3.b	odd	2	1		8712.2.a.c		1
4.b	odd	2	1		1936.2.a.f		1
8.b	even	2	1		7744.2.a.r		1
8.d	odd	2	1		7744.2.a.p		1
11.b	odd	2	1		968.2.a.b	✓	1
11.c	even	5	4		968.2.i.g		4
11.d	odd	10	4		968.2.i.h		4
33.d	even	2	1		8712.2.a.b		1
44.c	even	2	1		1936.2.a.g		1
88.b	odd	2	1		7744.2.a.q		1
88.g	even	2	1		7744.2.a.s		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
968.2.a.b	✓	1	11.b	odd	2	1
968.2.a.c	yes	1	1.a	even	1	1	trivial
968.2.i.g		4	11.c	even	5	4
968.2.i.h		4	11.d	odd	10	4
1936.2.a.f		1	4.b	odd	2	1
1936.2.a.g		1	44.c	even	2	1
7744.2.a.p		1	8.d	odd	2	1
7744.2.a.q		1	88.b	odd	2	1
7744.2.a.r		1	8.b	even	2	1
7744.2.a.s		1	88.g	even	2	1
8712.2.a.b		1	33.d	even	2	1
8712.2.a.c		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(968))$ :

T_{3}

T_{7} - 4

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T$ T
$5$	$T - 3$ T - 3
$7$	$T - 4$ T - 4
$11$	$T$ T
$13$	$T - 3$ T - 3
$17$	$T - 3$ T - 3
$19$	$T - 4$ T - 4
$23$	$T + 8$ T + 8
$29$	$T + 5$ T + 5
$31$	$T + 4$ T + 4
$37$	$T - 11$ T - 11
$41$	$T - 7$ T - 7
$43$	$T + 12$ T + 12
$47$	$T + 8$ T + 8
$53$	$T + 1$ T + 1
$59$	$T + 4$ T + 4
$61$	$T + 2$ T + 2
$67$	$T - 4$ T - 4
$71$	$T - 12$ T - 12
$73$	$T - 10$ T - 10
$79$	$T - 8$ T - 8
$83$	$T - 4$ T - 4
$89$	$T - 3$ T - 3
$97$	$T + 13$ T + 13
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