Properties

Label 20181.2.a.bh
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,-2,2,6,2,8,-4,-2,0,2,0,6,8,2,0,16,-2,-8,-12,-6,6, -16,-2,2,12,-8,0,-6,4,16,0,2,-8,-16,0,8,0,-2,-8,-12,0,-16,-4,-6,2,6,-8, -32,4,-2,-8,6,0,0,12,-16,-8,0,2,-14,-32,8,-20,24,12,8,0,6,-8,-4,-6,-32, -4,16,16,0,2,8,-16,-2,16,-4,-12,-16,-8,8,0,-20,0,-20,-32,6,-4,2,-4,6] 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9} + 8 q^{10} - 4 q^{11} - 2 q^{12} + 2 q^{14} + 6 q^{16} + 8 q^{17} + 2 q^{18} + 16 q^{20} - 2 q^{21} - 8 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 4 q^{99}+O(q^{100}) \) 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.