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Properties

Label 38025.2.a.iz
Level $38025$
Weight $2$
Character orbit 38025.a
Self dual yes
Analytic conductor $303.631$
Dimension $16$

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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] = [38025,2,Mod(1,38025)] 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("38025.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38025, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 38025 = 3^{2} \cdot 5^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38025.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0,0,20,0,0,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,-12,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,-32,0,0,0,0,0,-24,0,0,0,0,0,0,0,0,0,0,0,-56, 0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,52,0,0,-128,0,0,0,0,0,-60,0,0,0,0,0, -80,0,0,0,0,0,0] 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: \(303.631153686\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 50x^{14} + 913x^{12} - 7496x^{10} + 27772x^{8} - 42704x^{6} + 24964x^{4} - 4592x^{2} + 256 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 16 q + 20 q^{4} + 20 q^{16} - 12 q^{22} - 32 q^{43} - 24 q^{49} - 56 q^{61} + 4 q^{64} + 52 q^{79} - 128 q^{82} - 60 q^{88} - 80 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.