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Properties

Label 12482.2.a.y
Level $12482$
Weight $2$
Character orbit 12482.a
Self dual yes
Analytic conductor $99.669$
Dimension $4$

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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 = [4,4,-2,4,0,-2,-1,4,-6,0,-7,-2,-1,-1,5,4,-7,-6,-10,0,3,-7,6,-2, 6,-1,4,-1,8,5,-9,4,6,-7,13,-6,-12,-10,-2,0,19,3,-6,-7,-5,6,4,-2,5,6,11, -1,0,4,13,-1,5,8,21,5,4,-9,-1,4,-13,6,5,-7,-3,13,0,-6,-25,-12,-3,-10,-18, -2,0,0,-4,19,-18,3,-3,-6,-14,-7,3,-5,20,6,7,4,0,-2,-22,5,8,6] 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: \(99.6692718030\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{5}, \sqrt{21})\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 13x^{2} + 16 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{6} - q^{7} + 4 q^{8} - 6 q^{9} - 7 q^{11} - 2 q^{12} - q^{13} - q^{14} + 5 q^{15} + 4 q^{16} - 7 q^{17} - 6 q^{18} - 10 q^{19} + 3 q^{21} - 7 q^{22} + 6 q^{23}+ \cdots + 8 q^{99}+O(q^{100}) \) 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.