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Properties

Label 17689.2.a.g
Level $17689$
Weight $2$
Character orbit 17689.a
Self dual yes
Analytic conductor $141.247$
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] = [17689,2,Mod(1,17689)] 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("17689.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17689, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 17689 = 7^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17689.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,-2,1,0,0,0,-3,0,-5,0,0,0,0,4,7,0,0,-2,0,0,-4,0,-4,0,0, 0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,-1,10,-3,0,-13,0,0,0,0,0,0,0,-5,0,0,0,0, 0,-15,0,0,-8,0,0,0,-14,0,0,0,0,11,0,0,0,0,0,0,4,9,0,16,0,7,0,0,0,0,0,0, 8,0,0,0,0,0,0,15,8] 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: \(141.247376135\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: not computed

$q$-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)
 
\(f(q)\) \(=\) \( q - 2 q^{4} + q^{5} - 3 q^{9} - 5 q^{11} + 4 q^{16} + 7 q^{17} - 2 q^{20} - 4 q^{23} - 4 q^{25} + 6 q^{36} - q^{43} + 10 q^{44} - 3 q^{45} - 13 q^{47} - 5 q^{55} - 15 q^{61} - 8 q^{64} - 14 q^{68} + 11 q^{73}+ \cdots + 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(7\) \( -1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.