Properties

Label 42135.2.a.k
Level 4213542135
Weight 22
Character orbit 42135.a
Self dual yes
Analytic conductor 336.450336.450
Dimension 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [42135,2,Mod(1,42135)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42135, 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("42135.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 42135=35532 42135 = 3 \cdot 5 \cdot 53^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 42135.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: 336.449668917336.449668917
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: not computed
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+q2+q3q4q5+q63q8+q9q104q11q122q13q15q16+2q17+q184q19+q204q223q24+q25+4q99+O(q100) q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{8} + q^{9} - q^{10} - 4 q^{11} - q^{12} - 2 q^{13} - q^{15} - q^{16} + 2 q^{17} + q^{18} - 4 q^{19} + q^{20} - 4 q^{22} - 3 q^{24} + q^{25}+ \cdots - 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
33 1 -1
55 +1 +1
5353 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.