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Properties

Label 36992.2.a.bw
Level $36992$
Weight $2$
Character orbit 36992.a
Self dual yes
Analytic conductor $295.383$
Dimension $5$

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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] = [36992,2,Mod(1,36992)] 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("36992.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(36992, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 36992 = 2^{7} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 36992.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [5,0,0,0,2,0,-2,0,9,0,10,0,-4,0,-10,0,0,0,-10,0,-14,0,8,0,11, 0,-6,0,14,0,-4,0,0,0,-26,0,-6,0,30,0,-10,0,4,0,18,0,-6,0,5,0,0,0,-30,0, -2,0,0,0,4,0,-2,0,-12,0,-32,0,-18,0,10,0,42,0,6,0,-8,0,2,0,0,0,53,0,-36, 0,0,0,-46,0,10,0,2,0,-2,0,-4,0,14,0,80,0] 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: \(295.382607157\)
Dimension: \(5\)
Coefficient field: 5.5.135076.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 2 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 5 q + 2 q^{5} - 2 q^{7} + 9 q^{9} + 10 q^{11} - 4 q^{13} - 10 q^{15} - 10 q^{19} - 14 q^{21} + 8 q^{23} + 11 q^{25} - 6 q^{27} + 14 q^{29} - 4 q^{31} - 26 q^{35} - 6 q^{37} + 30 q^{39} - 10 q^{41} + 4 q^{43}+ \cdots + 80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.