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Properties

Label 15210.2.a.cm
Level $15210$
Weight $2$
Character orbit 15210.a
Self dual yes
Analytic conductor $121.452$
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] = [15210,2,Mod(1,15210)] 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("15210.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15210, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 15210 = 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 15210.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,0,2,-2,0,0,2,0,-2,-6,0,0,0,0,2,0,0,0,-2,0,-6,0,0,2,0,0,0, 0,0,0,2,0,0,0,0,0,0,0,-2,12,0,2,-6,0,0,6,0,-14,2,0,0,0,0,6,0,0,0,18,0, -16,0,0,2,0,0,0,0,0,0,-12,0,0,0,0,0,0,0,-22,-2,0,12,12,0,0,2,0,-6,0,0, 0,0,0,6,0,0,0,-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: \(121.452461474\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{3}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: not computed

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{8} - 2 q^{10} - 6 q^{11} + 2 q^{16} - 2 q^{20} - 6 q^{22} + 2 q^{25} + 2 q^{32} - 2 q^{40} + 12 q^{41} + 2 q^{43} - 6 q^{44} + 6 q^{47} - 14 q^{49} + 2 q^{50} + 6 q^{55}+ \cdots - 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(13\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.