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Properties

Label 33120.2.a.cr
Level $33120$
Weight $2$
Character orbit 33120.a
Self dual yes
Analytic conductor $264.465$
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] = [33120,2,Mod(1,33120)] 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("33120.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33120, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 33120 = 2^{5} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33120.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [5,0,0,0,5,0,-5,0,0,0,-4,0,0,0,0,0,13,0,2,0,0,0,-5,0,5,0,0,0, -1,0,-3,0,0,0,-5,0,1,0,0,0,7,0,0,0,0,0,-18,0,-4,0,0,0,1,0,-4,0,0,0,-19, 0,8,0,0,0,0,0,1,0,0,0,-11,0,-26,0,0,0,-2,0,0,0,0,0,-19,0,13,0,0,0,20,0, 12,0,0,0,2,0,-10,0,0,0] 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: \(264.464531494\)
Dimension: \(5\)
Coefficient field: 5.5.792644.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 7x^{3} + 4x^{2} + 4x - 2 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 5 q + 5 q^{5} - 5 q^{7} - 4 q^{11} + 13 q^{17} + 2 q^{19} - 5 q^{23} + 5 q^{25} - q^{29} - 3 q^{31} - 5 q^{35} + q^{37} + 7 q^{41} - 18 q^{47} - 4 q^{49} + q^{53} - 4 q^{55} - 19 q^{59} + 8 q^{61} + q^{67}+ \cdots - 10 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(5\) \( -1 \)
\(23\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.