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Properties

Label 27885.2.a.ec
Level $27885$
Weight $2$
Character orbit 27885.a
Self dual yes
Analytic conductor $222.663$
Dimension $36$

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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 = [36,3,36,45,36,3,20,9,36,3,36,45,0,18,36,55,6,3,40,45,20,3,26, 9,36,0,36,58,5,3,34,26,36,38,20,45,46,24,0,9,-1,18,-12,45,36,46,22,55, 68,3,6,0,31,3,36,20,40,27,46,45,2,3,20,35,0,3,79,-25,26,18,28,9,76,-18, 36,68,20,0,22,55,36,-54,34,58,6,30,5,9,34,3,0,42,34,-27,40,26,92,0,36, 45] 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: \(36\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 3 q^{2} + 36 q^{3} + 45 q^{4} + 36 q^{5} + 3 q^{6} + 20 q^{7} + 9 q^{8} + 36 q^{9} + 3 q^{10} + 36 q^{11} + 45 q^{12} + 18 q^{14} + 36 q^{15} + 55 q^{16} + 6 q^{17} + 3 q^{18} + 40 q^{19} + 45 q^{20}+ \cdots + 36 q^{99}+O(q^{100}) \) 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.