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Properties

Label 17689.2.a.cj
Level $17689$
Weight $2$
Character orbit 17689.a
Self dual yes
Analytic conductor $141.247$
Dimension $15$

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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 = [15,3,-6,15,0,0,0,9,21,-6,0,-18,-18,0,-12,-9,9,15,0,15,0,9,-6, -18,21,-45,-27,0,9,-21,-12,36,-57,-3,0,57,18,0,-12,-15,-42,0,-12,51,27, 6,3,-42,0,-3,-6,-36,33,45,-6,0,0,-30,-18,-18,6,-12,0,-3,45,-33,24,51,-15, 0,-6,-9,3,-9,-72,0,0,27,-60,-18,27,-36,12,0,-27,51,24,36,-72,3,0,-60,60, -21,0,-33,-39,0,54,9] 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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 3 x^{14} - 18 x^{13} + 56 x^{12} + 126 x^{11} - 417 x^{10} - 420 x^{9} + 1572 x^{8} + \cdots + 107 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 15 q + 3 q^{2} - 6 q^{3} + 15 q^{4} + 9 q^{8} + 21 q^{9} - 6 q^{10} - 18 q^{12} - 18 q^{13} - 12 q^{15} - 9 q^{16} + 9 q^{17} + 15 q^{18} + 15 q^{20} + 9 q^{22} - 6 q^{23} - 18 q^{24} + 21 q^{25} - 45 q^{26}+ \cdots + 54 q^{99}+O(q^{100}) \) 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.