Properties

Label 20181.2.a.bg
Level $20181$
Weight $2$
Character orbit 20181.a
Self dual yes
Analytic conductor $161.146$
Dimension $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [20181,2,Mod(1,20181)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("20181.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20181, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 20181 = 3 \cdot 7 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 20181.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,-2,2,0,-2,-2,6,2,0,0,-2,4,-2,0,6,4,2,0,0,2,4,-8,-6,-10,12, -2,-2,-4,0,0,-6,0,-4,0,2,16,8,-4,0,-16,2,-4,8,0,-4,12,-6,2,-10,-4,20,4, -2,0,-6,0,0,4,0,-12,0,-2,-14,0,-4,12,-12,8,0,-16,6,28,12,10,16,0,-12,-20, 0,2,-8,24,2,0,24,4,4,4,0,-4,0,0,12,0,6,4,2,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.146096319\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{2}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{12} + 4 q^{13} - 2 q^{14} + 6 q^{16} + 4 q^{17} + 2 q^{18} + 2 q^{21} + 4 q^{22} - 8 q^{23} - 6 q^{24} - 10 q^{25} + 12 q^{26}+ \cdots + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(7\) \( +1 \)
\(31\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.