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Properties

Label 36992.2.a.e
Level $36992$
Weight $2$
Character orbit 36992.a
Self dual yes
Analytic conductor $295.383$
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] = [36992,2,Mod(1,36992)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
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")
 
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);
 
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 = [2,0,-4,0,-4,0,-4,0,2,0,-4,0,-8,0,8,0,0,0,-4,0,8,0,-12,0,2,0, 8,0,12,0,-4,0,8,0,16,0,4,0,16,0,8,0,12,0,-4,0,-8,0,10,0,0,0,-16,0,16,0, 8,0,4,0,-20,0,-4,0,8,0,20,0,24,0,-12,0,8,0,-4,0,24,0,-20,0,-22,0,4,0,0, 0,-24,0,-16,0,0,0,8,0,0,0,0,0,-4,0] 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: \(2\)
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: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 2 q - 4 q^{3} - 4 q^{5} - 4 q^{7} + 2 q^{9} - 4 q^{11} - 8 q^{13} + 8 q^{15} - 4 q^{19} + 8 q^{21} - 12 q^{23} + 2 q^{25} + 8 q^{27} + 12 q^{29} - 4 q^{31} + 8 q^{33} + 16 q^{35} + 4 q^{37} + 16 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) \) 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.