LMFDB - Newform orbit 7650.2.a.ba

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7650,2,Mod(1,7650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7650, 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("7650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$7650 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	7650.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:	$61.0855575463$
Analytic rank:	$1$
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 - q^{2} + q^{4} + 2 q^{7} - q^{8} + 2 q^{11} - 2 q^{14} + q^{16} + q^{17} - 6 q^{19} - 2 q^{22} - 3 q^{23} + 2 q^{28} + 6 q^{29} - 6 q^{31} - q^{32} - q^{34} - 5 q^{37} + 6 q^{38} + 9 q^{41} - 6 q^{43}+ \cdots + 3 q^{98}+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

2.00000

−1.00000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$+1$
$5$	$-1$
$17$	$-1$

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	7650.2.a.ba	yes	1
3.b	odd	2	1		7650.2.a.ce	yes	1
5.b	even	2	1		7650.2.a.bq	yes	1
15.d	odd	2	1		7650.2.a.h	✓	1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7650.2.a.h	✓	1	15.d	odd	2	1
7650.2.a.ba	yes	1	1.a	even	1	1	trivial
7650.2.a.bq	yes	1	5.b	even	2	1
7650.2.a.ce	yes	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 $S_{2}^{\mathrm{new}}(\Gamma_0(7650))$ :

T_{7} - 2

T_{11} - 2

T_{13}

T_{19} + 6

T_{23} + 3

T_{29} - 6

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 1$ T + 1
$3$	$T$ T
$5$	$T$ T
$7$	$T - 2$ T - 2
$11$	$T - 2$ T - 2
$13$	$T$ T
$17$	$T - 1$ T - 1
$19$	$T + 6$ T + 6
$23$	$T + 3$ T + 3
$29$	$T - 6$ T - 6
$31$	$T + 6$ T + 6
$37$	$T + 5$ T + 5
$41$	$T - 9$ T - 9
$43$	$T + 6$ T + 6
$47$	$T - 2$ T - 2
$53$	$T + 3$ T + 3
$59$	$T + 9$ T + 9
$61$	$T - 7$ T - 7
$67$	$T + 14$ T + 14
$71$	$T + 3$ T + 3
$73$	$T$ T
$79$	$T + 6$ T + 6
$83$	$T + 9$ T + 9
$89$	$T - 12$ T - 12
$97$	$T + 8$ T + 8
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