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Properties

Label 33600.2.a.jx
Level $33600$
Weight $2$
Character orbit 33600.a
Self dual yes
Analytic conductor $268.297$
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] = [33600,2,Mod(1,33600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("33600.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 33600 = 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33600.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,0,-3,0,0,0,3,0,3,0,-2,0,-2,0,0,0,0,0,-2,0,-3,0,8,0,0,0,-3, 0,-2,0,-2,0,2,0,0,0,4,0,2,0,14,0,-12,0,0,0,8,0,3,0,0,0,-14,0,0,0,2,0,-8, 0,-2,0,3,0,0,0,0,0,-8,0,-6,0,6,0,0,0,-2,0,-20,0,3,0,-8,0,0,0,2,0,2,0,-2, 0,2,0,0,0,-14,0,-2,0] 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: \(268.297350792\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{3} + 3 q^{7} + 3 q^{9} - 2 q^{11} - 2 q^{13} - 2 q^{19} - 3 q^{21} + 8 q^{23} - 3 q^{27} - 2 q^{29} - 2 q^{31} + 2 q^{33} + 4 q^{37} + 2 q^{39} + 14 q^{41} - 12 q^{43} + 8 q^{47} + 3 q^{49} - 14 q^{53}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(7\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.