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Properties

Label 42320.2.a.dq
Level $42320$
Weight $2$
Character orbit 42320.a
Self dual yes
Analytic conductor $337.927$
Dimension $4$

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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] = [42320,2,Mod(1,42320)] 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("42320.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42320, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 42320 = 2^{4} \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 42320.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,2,0,4,0,2,0,6,0,10,0,-2,0,2,0,-14,0,2,0,-20,0,0,0,4,0,8, 0,-4,0,10,0,22,0,2,0,-8,0,16,0,-2,0,0,0,6,0,-8,0,6,0,-18,0,-24,0,10,0, -40,0,8,0,-38,0,-8,0,-2,0,12,0,0,0,10,0,0,0,2,0,-16,0,-20,0,-8,0,-4,0, -14,0,4,0,4,0,-22,0,-12,0,2,0,-10,0,26,0] 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: \(337.926901354\)
Dimension: \(4\)
Coefficient field: 4.4.13888.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 7x^{2} + 6x + 9 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + 2 q^{3} + 4 q^{5} + 2 q^{7} + 6 q^{9} + 10 q^{11} - 2 q^{13} + 2 q^{15} - 14 q^{17} + 2 q^{19} - 20 q^{21} + 4 q^{25} + 8 q^{27} - 4 q^{29} + 10 q^{31} + 22 q^{33} + 2 q^{35} - 8 q^{37} + 16 q^{39}+ \cdots + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( -1 \)
\(23\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.