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Properties

Label 17787.2.a.o
Level $17787$
Weight $2$
Character orbit 17787.a
Self dual yes
Analytic conductor $142.030$
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] = [17787,2,Mod(1,17787)] 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("17787.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17787, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 17787 = 3 \cdot 7^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17787.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,-1,2,-1,0,3,1,-2,0,-1,-2,0,2,-1,-2,-1,0,-2,0,0,8,3,-1, 2,1,0,6,-2,8,-5,0,2,0,-1,6,0,-2,6,-2,0,0,0,2,-8,-8,-1,0,1,-2,2,6,-1,0, 0,0,-6,4,-2,6,-8,0,7,-4,0,-4,2,8,0,0,3,-14,-6,-1,0,0,2,4,-2,1,2,12,0,-4, 0,6,0,6,-2,0,-8,8,8,0,-5,-2,0,0,1] 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: \(142.029910075\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + q^{9} - 2 q^{10} - q^{12} - 2 q^{13} + 2 q^{15} - q^{16} - 2 q^{17} - q^{18} - 2 q^{20} + 8 q^{23} + 3 q^{24} - q^{25} + 2 q^{26} + q^{27}+ \cdots - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(7\) \( -1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.