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Properties

Label 27885.2.a.cf
Level $27885$
Weight $2$
Character orbit 27885.a
Self dual yes
Analytic conductor $222.663$
Dimension $6$

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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] = [27885,2,Mod(1,27885)] 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("27885.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27885, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 27885 = 3 \cdot 5 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27885.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,-4,-6,0,-6,4,9,-6,6,4,6,0,0,-6,6,4,-2,-4,-13,0,-9,-4,-6,6, 6,0,-6,7,17,-4,-9,14,-6,-1,-9,0,3,11,0,6,15,6,-1,0,-6,-3,-12,-4,27,-4, 2,0,-19,4,-6,-23,13,-30,26,0,-12,-8,9,-22,0,4,1,14,6,6,10,-6,20,-37,-6, 7,9,0,-40,-4,6,11,12,-7,2,10,-17,-6,37,4,0,0,9,15,13,-14,-28,-25,6,0] 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: \(222.662846036\)
Dimension: \(6\)
Coefficient field: 6.6.78928073.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 25x^{4} + 21x^{3} + 187x^{2} - 93x - 433 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q - 4 q^{2} - 6 q^{3} - 6 q^{5} + 4 q^{6} + 9 q^{7} - 6 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} - 13 q^{19} - 9 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( +1 \)
\(11\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.