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Properties

Label 27930.2.a.ch
Level $27930$
Weight $2$
Character orbit 27930.a
Self dual yes
Analytic conductor $223.022$
Dimension $1$

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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] = [27930,2,Mod(1,27930)] 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("27930.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27930, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 27930 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27930.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,1,-1,-1,0,1,1,-1,2,-1,-4,0,1,1,2,1,1,-1,0,2,4,-1,1,-4, -1,0,0,1,8,1,-2,2,0,1,8,1,4,-1,8,0,-6,2,-1,4,12,-1,0,1,-2,-4,-6,-1,-2, 0,-1,0,0,1,-2,8,0,1,4,-2,8,2,-4,0,-8,1,-14,8,-1,1,0,4,0,-1,1,8,-4,0,-2, -6,0,2,0,-1,0,4,-8,12,-1,-1,12,0,2,1] 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: \(223.022172845\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} + 2 q^{11} - q^{12} - 4 q^{13} + q^{15} + q^{16} + 2 q^{17} + q^{18} + q^{19} - q^{20} + 2 q^{22} + 4 q^{23} - q^{24} + q^{25}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(19\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.