LMFDB - Newform orbit 960.2.a.l

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(1,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("960.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$960 = 2^{6} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	960.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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 15)
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^{3} - q^{5} + q^{9} + 4 q^{11} + 2 q^{13} - q^{15} + 2 q^{17} - 4 q^{19} + q^{25} + q^{27} + 2 q^{29} + 4 q^{33} + 10 q^{37} + 2 q^{39} + 10 q^{41} - 4 q^{43} - q^{45} + 8 q^{47} - 7 q^{49}+ \cdots + 4 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

1.00000

−1.00000

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	960.2.a.l		1
3.b	odd	2	1		2880.2.a.y		1
4.b	odd	2	1		960.2.a.a		1
5.b	even	2	1		4800.2.a.t		1
5.c	odd	4	2		4800.2.f.bf		2
8.b	even	2	1		15.2.a.a	✓	1
8.d	odd	2	1		240.2.a.d		1
12.b	even	2	1		2880.2.a.bc		1
16.e	even	4	2		3840.2.k.m		2
16.f	odd	4	2		3840.2.k.r		2
20.d	odd	2	1		4800.2.a.bz		1
20.e	even	4	2		4800.2.f.c		2
24.f	even	2	1		720.2.a.c		1
24.h	odd	2	1		45.2.a.a		1
40.e	odd	2	1		1200.2.a.e		1
40.f	even	2	1		75.2.a.b		1
40.i	odd	4	2		75.2.b.b		2
40.k	even	4	2		1200.2.f.h		2
56.h	odd	2	1		735.2.a.c		1
56.j	odd	6	2		735.2.i.d		2
56.p	even	6	2		735.2.i.e		2
72.j	odd	6	2		405.2.e.c		2
72.n	even	6	2		405.2.e.f		2
88.b	odd	2	1		1815.2.a.d		1
104.e	even	2	1		2535.2.a.j		1
120.i	odd	2	1		225.2.a.b		1
120.m	even	2	1		3600.2.a.u		1
120.q	odd	4	2		3600.2.f.e		2
120.w	even	4	2		225.2.b.b		2
136.h	even	2	1		4335.2.a.c		1
152.g	odd	2	1		5415.2.a.j		1
168.i	even	2	1		2205.2.a.i		1
184.e	odd	2	1		7935.2.a.d		1
264.m	even	2	1		5445.2.a.c		1
280.c	odd	2	1		3675.2.a.j		1
312.b	odd	2	1		7605.2.a.g		1
440.o	odd	2	1		9075.2.a.g		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
15.2.a.a	✓	1	8.b	even	2	1
45.2.a.a		1	24.h	odd	2	1
75.2.a.b		1	40.f	even	2	1
75.2.b.b		2	40.i	odd	4	2
225.2.a.b		1	120.i	odd	2	1
225.2.b.b		2	120.w	even	4	2
240.2.a.d		1	8.d	odd	2	1
405.2.e.c		2	72.j	odd	6	2
405.2.e.f		2	72.n	even	6	2
720.2.a.c		1	24.f	even	2	1
735.2.a.c		1	56.h	odd	2	1
735.2.i.d		2	56.j	odd	6	2
735.2.i.e		2	56.p	even	6	2
960.2.a.a		1	4.b	odd	2	1
960.2.a.l		1	1.a	even	1	1	trivial
1200.2.a.e		1	40.e	odd	2	1
1200.2.f.h		2	40.k	even	4	2
1815.2.a.d		1	88.b	odd	2	1
2205.2.a.i		1	168.i	even	2	1
2535.2.a.j		1	104.e	even	2	1
2880.2.a.y		1	3.b	odd	2	1
2880.2.a.bc		1	12.b	even	2	1
3600.2.a.u		1	120.m	even	2	1
3600.2.f.e		2	120.q	odd	4	2
3675.2.a.j		1	280.c	odd	2	1
3840.2.k.m		2	16.e	even	4	2
3840.2.k.r		2	16.f	odd	4	2
4335.2.a.c		1	136.h	even	2	1
4800.2.a.t		1	5.b	even	2	1
4800.2.a.bz		1	20.d	odd	2	1
4800.2.f.c		2	20.e	even	4	2
4800.2.f.bf		2	5.c	odd	4	2
5415.2.a.j		1	152.g	odd	2	1
5445.2.a.c		1	264.m	even	2	1
7605.2.a.g		1	312.b	odd	2	1
7935.2.a.d		1	184.e	odd	2	1
9075.2.a.g		1	440.o	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(960))$ :

T_{7}

T_{11} - 4

T_{13} - 2

T_{19} + 4

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T - 1$ T - 1
$5$	$T + 1$ T + 1
$7$	$T$ T
$11$	$T - 4$ T - 4
$13$	$T - 2$ T - 2
$17$	$T - 2$ T - 2
$19$	$T + 4$ T + 4
$23$	$T$ T
$29$	$T - 2$ T - 2
$31$	$T$ T
$37$	$T - 10$ T - 10
$41$	$T - 10$ T - 10
$43$	$T + 4$ T + 4
$47$	$T - 8$ T - 8
$53$	$T - 10$ T - 10
$59$	$T - 4$ T - 4
$61$	$T - 2$ T - 2
$67$	$T + 12$ T + 12
$71$	$T + 8$ T + 8
$73$	$T - 10$ T - 10
$79$	$T$ T
$83$	$T + 12$ T + 12
$89$	$T + 6$ T + 6
$97$	$T - 2$ T - 2
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