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Properties

Label 27690.2.a.bc
Level $27690$
Weight $2$
Character orbit 27690.a
Self dual yes
Analytic conductor $221.106$
Dimension $1$
CM no
Inner twists $1$

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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] = [27690,2,Mod(1,27690)] 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("27690.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27690, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 27690 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27690.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1,1,1,1,-4,1,1,1,2,1,1,-4,1,1,6,1,-4,1,-4,2,-2,1,1,1,1,-4, -6,1,-2,1,2,6,-4,1,2,-4,1,1,-8,-4,-8,2,1,-2,6,1,9,1,6,1,-4,1,2,-4,-4,-6, 2,1,0,-2,-4,1,1,2,-14,6,-2,-4,-1,1,-10,2,1,-4,-8,1,-12,1,1,-8,4,-4,6,-8, -6,2,-6,1,-4,-2,-2,6,-4,1,-8,9,2,1] 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: \(221.105763197\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} + 2 q^{11} + q^{12} + q^{13} - 4 q^{14} + q^{15} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} - 4 q^{21} + 2 q^{22}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( -1 \)
\(13\) \( -1 \)
\(71\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.