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Properties

Label 15800.2.a.p
Level $15800$
Weight $2$
Character orbit 15800.a
Self dual yes
Analytic conductor $126.164$
Dimension $8$

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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] = [15800,2,Mod(1,15800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15800, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("15800.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 15800 = 2^{3} \cdot 5^{2} \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 15800.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,3,0,0,0,4,0,13,0,-9,0,-2,0,0,0,6,0,-19,0,-22,0,26,0,0,0, 18,0,-17,0,-30,0,9,0,0,0,1,0,-14,0,-10,0,8,0,0,0,2,0,16,0,-15,0,-20,0, 0,0,-31,0,-9,0,17,0,13,0,0,0,23,0,-39,0,-27,0,-9,0,0,0,-8,0,8,0,24,0,-17, 0,0,0,-12,0,-22,0,-25,0,-17,0,0,0,-35,0,-41,0] 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: \(126.163635194\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 16x^{6} + 17x^{5} + 60x^{4} - 48x^{3} - 65x^{2} + 40x + 8 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 8 q + 3 q^{3} + 4 q^{7} + 13 q^{9} - 9 q^{11} - 2 q^{13} + 6 q^{17} - 19 q^{19} - 22 q^{21} + 26 q^{23} + 18 q^{27} - 17 q^{29} - 30 q^{31} + 9 q^{33} + q^{37} - 14 q^{39} - 10 q^{41} + 8 q^{43} + 2 q^{47}+ \cdots - 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( +1 \)
\(79\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.