LMFDB - Newform orbit 153.2.a.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(1,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("153.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$153 = 3^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	153.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:	$1.22171115093$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 51)
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^{4} - 3 q^{5} - 4 q^{7} + 3 q^{11} - q^{13} + 4 q^{16} + q^{17} - q^{19} + 6 q^{20} - 9 q^{23} + 4 q^{25} + 8 q^{28} - 6 q^{29} + 2 q^{31} + 12 q^{35} - 4 q^{37} + 3 q^{41} - 7 q^{43} - 6 q^{44}+ \cdots - 16 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

−2.00000

−3.00000

−4.00000

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$17$	$-1$

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	153.2.a.b		1
3.b	odd	2	1		51.2.a.a	✓	1
4.b	odd	2	1		2448.2.a.c		1
5.b	even	2	1		3825.2.a.i		1
7.b	odd	2	1		7497.2.a.j		1
8.b	even	2	1		9792.2.a.by		1
8.d	odd	2	1		9792.2.a.cd		1
12.b	even	2	1		816.2.a.g		1
15.d	odd	2	1		1275.2.a.d		1
15.e	even	4	2		1275.2.b.b		2
17.b	even	2	1		2601.2.a.f		1
21.c	even	2	1		2499.2.a.d		1
24.f	even	2	1		3264.2.a.r		1
24.h	odd	2	1		3264.2.a.a		1
33.d	even	2	1		6171.2.a.e		1
39.d	odd	2	1		8619.2.a.g		1
51.c	odd	2	1		867.2.a.c		1
51.f	odd	4	2		867.2.d.a		2
51.g	odd	8	4		867.2.e.e		4
51.i	even	16	8		867.2.h.c		8

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
51.2.a.a	✓	1	3.b	odd	2	1
153.2.a.b		1	1.a	even	1	1	trivial
816.2.a.g		1	12.b	even	2	1
867.2.a.c		1	51.c	odd	2	1
867.2.d.a		2	51.f	odd	4	2
867.2.e.e		4	51.g	odd	8	4
867.2.h.c		8	51.i	even	16	8
1275.2.a.d		1	15.d	odd	2	1
1275.2.b.b		2	15.e	even	4	2
2448.2.a.c		1	4.b	odd	2	1
2499.2.a.d		1	21.c	even	2	1
2601.2.a.f		1	17.b	even	2	1
3264.2.a.a		1	24.h	odd	2	1
3264.2.a.r		1	24.f	even	2	1
3825.2.a.i		1	5.b	even	2	1
6171.2.a.e		1	33.d	even	2	1
7497.2.a.j		1	7.b	odd	2	1
8619.2.a.g		1	39.d	odd	2	1
9792.2.a.by		1	8.b	even	2	1
9792.2.a.cd		1	8.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2}$ T2 acting on $S_{2}^{\mathrm{new}}(\Gamma_0(153))$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T$ T
$5$	$T + 3$ T + 3
$7$	$T + 4$ T + 4
$11$	$T - 3$ T - 3
$13$	$T + 1$ T + 1
$17$	$T - 1$ T - 1
$19$	$T + 1$ T + 1
$23$	$T + 9$ T + 9
$29$	$T + 6$ T + 6
$31$	$T - 2$ T - 2
$37$	$T + 4$ T + 4
$41$	$T - 3$ T - 3
$43$	$T + 7$ T + 7
$47$	$T - 6$ T - 6
$53$	$T - 6$ T - 6
$59$	$T + 6$ T + 6
$61$	$T - 8$ T - 8
$67$	$T + 4$ T + 4
$71$	$T + 12$ T + 12
$73$	$T - 2$ T - 2
$79$	$T + 10$ T + 10
$83$	$T - 6$ T - 6
$89$	$T$ T
$97$	$T + 16$ T + 16
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