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Properties

Label 17689.2.a.cd
Level $17689$
Weight $2$
Character orbit 17689.a
Self dual yes
Analytic conductor $141.247$
Dimension $12$

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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 = [12,-1,3,11,0,-6,0,-9,9,16,1,-2,6,0,9,9,8,-5,0,0,0,2,9,-8,14, 1,9,0,2,9,11,-24,3,6,0,7,14,0,10,42,20,0,-2,-2,-12,6,0,39,0,11,-21,11, -7,-43,9,0,0,-35,42,6,6,-19,0,-1,27,3,14,51,17,0,-1,-18,-21,25,31,0,0, -57,5,13,-28,-12,-5,0,27,-18,53,36,-1,27,0,72,-34,12,0,-94,31,0,-43,-7] 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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} - 17 x^{10} + 13 x^{9} + 106 x^{8} - 57 x^{7} - 294 x^{6} + 100 x^{5} + 350 x^{4} + \cdots + 3 \) Copy content Toggle raw display
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.

\(\operatorname{Tr}(f)(q) = \) \( 12 q - q^{2} + 3 q^{3} + 11 q^{4} - 6 q^{6} - 9 q^{8} + 9 q^{9} + 16 q^{10} + q^{11} - 2 q^{12} + 6 q^{13} + 9 q^{15} + 9 q^{16} + 8 q^{17} - 5 q^{18} + 2 q^{22} + 9 q^{23} - 8 q^{24} + 14 q^{25} + q^{26}+ \cdots - 43 q^{99}+O(q^{100}) \) 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.