Properties

Label 20691.2.a.a
Level $20691$
Weight $2$
Character orbit 20691.a
Self dual yes
Analytic conductor $165.218$
Dimension $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [20691,2,Mod(1,20691)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20691, 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("20691.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20691 = 3^{2} \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 20691.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: \(165.218466822\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
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)
 
\(f(q)\) \(=\) \( q - 2 q^{2} + 2 q^{4} - q^{5} - 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + 2 q^{4} - q^{5} - 3 q^{7} + 2 q^{10} + 6 q^{13} + 6 q^{14} - 4 q^{16} + 3 q^{17} + q^{19} - 2 q^{20} - 4 q^{23} - 4 q^{25} - 12 q^{26} - 6 q^{28} - 10 q^{29} + 2 q^{31} + 8 q^{32} - 6 q^{34} + 3 q^{35} + 8 q^{37} - 2 q^{38} - 8 q^{41} + q^{43} + 8 q^{46} - 3 q^{47} + 2 q^{49} + 8 q^{50} + 12 q^{52} + 6 q^{53} + 20 q^{58} - 7 q^{61} - 4 q^{62} - 8 q^{64} - 6 q^{65} + 8 q^{67} + 6 q^{68} - 6 q^{70} - 12 q^{71} + 11 q^{73} - 16 q^{74} + 2 q^{76} + 4 q^{80} + 16 q^{82} + 4 q^{83} - 3 q^{85} - 2 q^{86} - 10 q^{89} - 18 q^{91} - 8 q^{92} + 6 q^{94} - q^{95} - 2 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(11\) \( -1 \)
\(19\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.