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Properties

Label 11025.2.a.bs
Level $11025$
Weight $2$
Character orbit 11025.a
Self dual yes
Analytic conductor $88.035$
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] = [11025,2,Mod(1,11025)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11025, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 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("11025.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 11025 = 3^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 11025.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,-2,0,-2,0,0,0,6,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,-8,0,0,0,0,0, 0,0,0,-10,0,0,0,0,12,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0, 0,0,14,0,0,-24,0,0,0,-24,0,0,-12,0,0,0,0,24,0,0,0,0,0,0,0,0,0,0,0,0,8, 0,0,0,0,0,0,0,0] 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: \(88.0350682285\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{2}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q - 2 q^{2} - 2 q^{4} + 6 q^{8} - 2 q^{16} - 8 q^{23} - 10 q^{32} + 12 q^{37} + 8 q^{46} + 16 q^{53} + 14 q^{64} - 24 q^{67} - 24 q^{71} - 12 q^{74} + 24 q^{79} + 8 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(7\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.