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Properties

Label 12482.2.a.n
Level $12482$
Weight $2$
Character orbit 12482.a
Self dual yes
Analytic conductor $99.669$
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] = [12482,2,Mod(1,12482)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12482, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("12482.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 12482 = 2 \cdot 79^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 12482.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,-2,-1,2,-3,1,-5,-2,1,3,7,-1,1,5,-5,2,-2,-1,0,-3,9,-7,-10,1, 1,-1,-4,-5,8,5,12,-2,-10,2,1,1,5,0,-20,3,10,-9,-1,7,5,10,3,-1,5,-1,1,1, 4,4,-4,5,0,-8,4,-5,-15,-12,-9,2,18,10,-8,-2,18,-1,-6,-1,21,-5,19,0,-24, 20,0,-3,-14,-10,-20,9,3,1,-4,-7,19,-5,-22,-10,7,-3,0,1,-4,-5,10,1] 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: \(99.6692718030\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} + q^{6} - 5 q^{7} - 2 q^{8} + q^{9} + 3 q^{10} + 7 q^{11} - q^{12} + q^{13} + 5 q^{14} - 5 q^{15} + 2 q^{16} - 2 q^{17} - q^{18} - 3 q^{20} + 9 q^{21} - 7 q^{22}+ \cdots + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(79\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.