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Properties

Label 10890.2.a.dc
Level $10890$
Weight $2$
Character orbit 10890.a
Self dual yes
Analytic conductor $86.957$
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] = [10890,2,Mod(1,10890)] 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("10890.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10890, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10890 = 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10890.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,0,2,2,0,0,2,0,2,0,0,-5,0,0,2,-1,0,4,2,0,0,-3,0,2,-5,0,0, -11,0,-15,2,0,-1,0,0,-7,4,0,2,-6,0,1,0,0,-3,-9,0,-14,2,0,-5,4,0,0,0,0, -11,-9,0,-2,-15,0,2,-5,0,-23,-1,0,0,-4,0,0,-7,0,4,0,0,13,2,0,-6,-6,0,-1, 1,0,0,0,0,0,-3,0,-9,4,0,14,-14,0,2] 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: \(86.9570878012\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{5}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{8} + 2 q^{10} - 5 q^{13} + 2 q^{16} - q^{17} + 4 q^{19} + 2 q^{20} - 3 q^{23} + 2 q^{25} - 5 q^{26} - 11 q^{29} - 15 q^{31} + 2 q^{32} - q^{34} - 7 q^{37} + 4 q^{38}+ \cdots - 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.