Properties

Label 20181.2.a.cq
Level $20181$
Weight $2$
Character orbit 20181.a
Self dual yes
Analytic conductor $161.146$
Dimension $28$

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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 = [28,-3,-28,19,-2,3,-28,-12,28,-3,-1,-19,7,3,2,-7,-5,-3,-21,18, 28,5,-15,12,16,7,-28,-19,13,3,0,-22,1,16,2,19,41,8,-7,-11,0,-3,-18,-46, -2,26,-11,7,28,-39,5,-2,10,3,13,12,21,22,-64,-18,23,0,-28,-54,52,-5,-46, 21,15,3,-54,-12,82,25,-16,-37,1,-7,-5,-8,28,-11,14,19,-1,-6,-13,37,-25, -3,-7,37,0,17,-52,22,3,-3,-1,50] 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: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 3 q^{2} - 28 q^{3} + 19 q^{4} - 2 q^{5} + 3 q^{6} - 28 q^{7} - 12 q^{8} + 28 q^{9} - 3 q^{10} - q^{11} - 19 q^{12} + 7 q^{13} + 3 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 3 q^{18} - 21 q^{19} + 18 q^{20}+ \cdots - q^{99}+O(q^{100}) \) 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.