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Properties

Label 42320.2.a.co
Level $42320$
Weight $2$
Character orbit 42320.a
Self dual yes
Analytic conductor $337.927$
Dimension $3$

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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 = [3,0,-1,0,-3,0,3,0,4,0,8,0,-2,0,1,0,-11,0,5,0,4,0,0,0,3,0,-16, 0,5,0,-18,0,-23,0,-3,0,-7,0,-12,0,3,0,12,0,-4,0,3,0,4,0,-9,0,17,0,-8,0, -22,0,-6,0,-11,0,-23,0,2,0,4,0,0,0,-17,0,-31,0,-1,0,20,0,-7,0,11,0,-30, 0,11,0,-17,0,-19,0,-7,0,11,0,-5,0,-1,0,19,0] 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: \(3\)
Coefficient field: 3.3.761.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 6x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - q^{3} - 3 q^{5} + 3 q^{7} + 4 q^{9} + 8 q^{11} - 2 q^{13} + q^{15} - 11 q^{17} + 5 q^{19} + 4 q^{21} + 3 q^{25} - 16 q^{27} + 5 q^{29} - 18 q^{31} - 23 q^{33} - 3 q^{35} - 7 q^{37} - 12 q^{39} + 3 q^{41}+ \cdots + 19 q^{99}+O(q^{100}) \) 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.