Properties

Label 20181.2.a.cg
Level $20181$
Weight $2$
Character orbit 20181.a
Self dual yes
Analytic conductor $161.146$
Dimension $16$

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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 = [16,0,-16,16,0,0,16,0,16,-16,-4,-16,-16,0,0,20,-20,0,8,-16,-16, -4,8,0,16,-24,-16,16,-16,16,0,20,4,-20,0,16,-8,24,16,-28,-36,0,12,-16, 0,28,-24,-20,16,48,20,-12,0,0,-16,0,-8,0,0,16,8,0,16,36,4,4,28,-56,-8, -16,-32,0,-8,68,-16,44,-4,24,-4,-32,16,36,-28,-16,8,-52,16,-92,-16,-16, -16,36,0,52,-8,-20,28,0,-4,8] 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: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 24 x^{14} + 227 x^{12} - 4 x^{11} - 1082 x^{10} + 64 x^{9} + 2757 x^{8} - 340 x^{7} - 3650 x^{6} + \cdots - 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 16 q - 16 q^{3} + 16 q^{4} + 16 q^{7} + 16 q^{9} - 16 q^{10} - 4 q^{11} - 16 q^{12} - 16 q^{13} + 20 q^{16} - 20 q^{17} + 8 q^{19} - 16 q^{20} - 16 q^{21} - 4 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 16 q^{27}+ \cdots - 4 q^{99}+O(q^{100}) \) 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.